30:T75c5,viewof rubik = embed({ "$schema": "https://vega.github.io/schema/vega/v5.json", "width":width, "height":500, "background":"white", "signals":[ { "name":"size", "init":"40*(min(width,height)/400)" }, { "name":"cube_padding", "value":0.02 }, { "name":"cube_size", "value":3 }, { "name":"btn_reset_pressed", "on":[{"events":"@btn_reset:mousedown,@txt_reset:mousedown", "update":"true"}, {"events":"@btn_reset:mouseup,@txt_reset:mouseup", "update":"false"}] }, { "name":"btn_shuffle_pressed", "on":[{"events":"@btn_shuffle:mousedown,@txt_shuffle:mousedown", "update":"true"}, {"events":"@btn_shuffle:mouseup,@txt_shuffle:mouseup", "update":"false"}] }, { "name":"btn_solve_pressed", "on":[{"events":"@btn_solve:mousedown,@txt_solve:mousedown", "update":"true"}, {"events":"@btn_solve:mouseup,@txt_solve:mouseup", "update":"false"}] }, { "name":"reset", "on": [{"events":"@btn_reset:mousedown,@txt_reset:mousedown", "update":"setdata('points',[{iX:[]}])"}, {"events":"@btn_reset:mouseup,@txt_reset:mouseup", "update":"0"}] }, { "name":"shuffle", "init":"-1", "on":[{"events":"@btn_shuffle:mousedown,@txt_shuffle:mousedown", "update":"setdata('shuffle', [{id:[]}]) === 1 ? -1:-1"},{"events":"@btn_shuffle:mouseup,@txt_shuffle:mouseup", "update":"solve_index === -1 ? 0 : -1"},{"events":"timer{50}", "update":"shuffle !== -1 && shuffle < 9 ? length(data('unfinished'))>0 ? shuffle : shuffle+1: -1"}] }, { "name":"shuffle_current", "on":[{"events":{"signal": "shuffle"}, "update":"shuffle !== -1 && shuffle <=9 ? data('shuffle')[shuffle]:null"}] }, { "name":"solve_index", "init":"-1", "on":[{"events":"@btn_solve:mouseup,@txt_solve:mouseup", "update":"length(data('history'))>0 ? solve_index === -1 ? length(data('history')) - 1 : solve_index : -1"},{"events":"timer{500}", "update":"solve_index >=0 && length(data('unfinished')) === 0 && solve_index !== -1 && solve_current_remaining === solve_current_completed ? solve_index - 1 : solve_index"},{"events":{"signal":"reset"},"update":"-1"}] }, { "name":"solve_current", "on":[{"events":{"signal":"solve_index"}, "update":"solve_index !==-1 ? data('history')[solve_index]: null"}] }, { "name":"solve_current_remaining", "on":[{"events":{"signal":"solve_current"}, "update":"solve_current !== null ? abs(round(solve_current.angle/90)): 0"}] }, { "name":"solve_current_rotation", "update":"solve_index !==-1 && solve_current!=null ? merge(solve_current,{angle:solve_current.angle < 0 ? 5 : -5}):{angle:0, axis:null, iX:-1, iY:-1, iZ:-1}", "on":[{"events":"timer{25}","update":"solve_index !==-1 && solve_current!=null && (length(data('unfinished'))> 0 || (solve_current_rotation.angle === 0 && solve_current_remaining > solve_current_completed)) ? merge(solve_current,{angle:solve_current.angle < 0 ? 5 : -5}):{angle:0, axis:null, iX:-1, iY:-1, iZ:-1}"}] }, { "name":"solve_current_completed", "on":[{"events":{"signal":"solve_current"},"update":"0"},{"events":{"signal":"solve_current_rotation"}, "update":"solve_current_rotation.angle === 0 && solve_current_completed >=0 && solve_current_remaining > solve_current_completed? solve_current_completed + 1 : solve_current_completed"}] }, { "name":"scale", "value":1, "bind":{"input":"range","min": 0, "max": 2, "step": 0.1}, "on":[{"events":"view:mousewheel", "update":"max(0, min(2, scale + (event.wheelDelta > 0 ? 0.1 : -0.1)))"}] }, { "name":"angle_HOR", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_HOR + (cube_changing ? 0 : ((event.movementX < 0) ^ (rotation_VER > 180) ? 5 : (event.movementX > 0) ^(rotation_VER > 180) ? -5 : 0))"}] }, { "name":"validAngle_HOR", "update":"angle_HOR % 360 <0 ? 360 + angle_HOR % 360 : angle_HOR % 360" }, { "name":"angle_VER", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_VER + ( cube_changing ? 0 :(event.movementY < 0 ? 5 : event.movementY > 0 ? -5 : 0))"}] }, { "name":"validAngle_VER", "update":"angle_VER % 360 <0 ? 360 + angle_VER % 360 : angle_VER % 360" }, { "name":"angle_Line", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "force": true,"update":"rotation_Line.angle === 0 && selected !=null ? ((selected.axis === 'z' ? (event.movementX < 0 ^ (rotation_VER > 180) ? 1 : event.movementX === 0 ? 0 : -1) : (selected.axis === 'x' ? (event.movementY < 0 ^ isYZBack ^ (rotation_VER > 180) ? 1 : event.movementY === 0 ? 0 : -1) : (selected.axis === 'y' ? (event.movementY < 0 ^ isXZBack ^ (rotation_VER > 180) ? 1 : event.movementY === 0 ? 0 : -1) : 0)))*10) : 0"}] }, { "name":"completion_Angle", "on":[{"events":{"signal":"last_Rotation"}, "update":"last_Rotation !== null && last_Rotation.rotation.a % 90 !== 0? {angle: last_Rotation.rotation.a % 90 === 0 ? 0 : abs(last_Rotation.rotation.a) % 90 < 40 ? -(last_Rotation.rotation.a % 90) : (last_Rotation.rotation.a < 0 ? -90 : 90) - last_Rotation.rotation.a % 90, axis: last_Rotation.rotation.r, iX:last_Rotation.iX, iY: last_Rotation.iY, iZ: last_Rotation.iZ}:{angle:0, axis:null, iX:-1, iY:-1, iZ:-1}"},{"events":"view:mousedown", "update":"selected !=null ? {angle:0, axis: selected.axis, iX: selected.iX, iY:selected.iY, iZ:selected.iZ}:{angle:0, axis:null, iX: -1, iY: -1, iZ: -1}"}] }, { "name":"last_Rotation", "on":[{"events":{"signal":"cube_changing"}, "update":"cube_changing? null : length(data('unfinished'))>0 ? data('unfinished')[0] : null"},{"events":{"signal":"reset"},"update":"null"}] }, { "name":"history_Rotation", "update":"shuffle === -1 ? null : history_Rotation", "on": [ {"events":{"signal":"solve_index"},"update":"solve_index === -1 ? null: history_Rotation"}, {"events":{"signal":"shuffle_current"}, "update":"isValid(shuffle_current) ? shuffle_current.rotation : history_Rotation"}, {"events":{"signal":"last_Rotation || completion_Angle"}, "update":"completion_Angle !=null && last_Rotation!=null ? completion_Angle.axis !== null ? merge(completion_Angle, {angle:completion_Angle.angle + last_Rotation.rotation.a}) : {angle:last_Rotation.rotation.a,axis: last_Rotation.rotation.r, iX: last_Rotation.iX, iY: last_Rotation.iY, iZ: last_Rotation.iZ} : history_Rotation"}, {"events":{"signal":"reset"},"update":"null"} ] }, { "name":"clear_history", "on":[{"events":{"signal":"reset"}, "update":"reset"}, { "events":{"signal":"solve_index"}, "update":"solve_index === -1" }] }, { "name":"rotation_Line", "value":{"angle":0, "axis":null, "iX":-1, "iY":-1, "iZ":-1}, "on":[{"events":{"signal":"angle_Line"}, "update":"selected !== null ? {angle:angle_Line, axis : selected.axis, iX: selected.iX, iY:selected.iY, iZ:selected.iZ}: {angle:0, axis:null, iX:-1, iY:-1, iZ:-1}"},{"events":{"signal":"completion_Angle"}, "update":"completion_Angle"},{"events":{"signal":"shuffle_current"}, "update":"shuffle_current!=null ? shuffle_current.rotation : {angle:0, axis:null, iX:-1, iY:-1, iZ:-1}"},{"events":{"signal":"solve_current_rotation"}, "update":"solve_current_rotation", "force": true}] }, { "name":"rotation_HOR", "value":45, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_HOR"}, "update":"validAngle_HOR"}] }, { "name":"rotation_VER", "value":65, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_VER"}, "update":"validAngle_VER"}] }, { "name":"qrAngle_HOR", "init":"PI*(rotation_HOR)/360", "on": [{"events":{"signal":"-rotation_HOR"}, "update":"PI*(rotation_HOR)/360"}] }, { "name":"qrAngle_VER", "init":"PI*(rotation_VER)/360", "on": [{"events":{"signal":"rotation_VER"}, "update":"PI*(rotation_VER)/360"}] }, { "name":"qrAngle_Line", "init":"PI*(rotation_Line.angle)/360", "on": [{"events":{"signal":"rotation_Line"}, "update":"PI*(rotation_Line.angle)/360"}] }, { "name":"qrw0", "update":"cos(qrAngle_VER)" }, { "name":"qrw1", "update":"cos(qrAngle_HOR)" }, { "name":"qrx0", "update":"sin(qrAngle_VER)" }, { "name":"qrz1", "update":"sin(qrAngle_HOR)" }, { "name":"q", "update":"{x:qrx0*qrw1, y:-qrx0*qrz1, z:qrw0*qrz1, w: qrw0*qrw1}" }, { "name":"q_1", "update":"{x:-q.x, y:-q.y, z: -q.z, w: q.w}" }, { "name":"isYZBack", "update":"{z: 2*(q.x * q.z) - 2*(q.w * q.y)}.z < 0" }, { "name":"isXZBack", "update":"{z: 2*(q.y * q.z) + 2 *(q.w * q.x)}.z < 0" }, { "name":"isXYBack", "update":"{z: (q.z*q.z) - (q.y*q.y) - (q.x*q.x) + (q.w*q.w)}.z < 0" }, { "name":"qLine", "update":"{x: (rotation_Line.axis === 'y' ? sin(qrAngle_Line) : 0), y:(rotation_Line.axis === 'x' ? sin(-qrAngle_Line) : 0), z:(rotation_Line.axis === 'z' ? sin(qrAngle_Line) : 0), w : (rotation_Line.axis !==null ? cos(qrAngle_Line) : 1)}" }, { "name":"qLine_1", "update":"{x: -qLine.x, y: -qLine.y, z: -qLine.z, w: qLine.w}" }, { "name":"cube_changing", "init":"false", "on":[{"events":"view:mousedown", "update":"selected!=null"},{"events":"view:mouseup", "update":"false"}] }, { "name":"selected", "init":"null", "on":[ {"events":"@face:mousemove", "update":"event.buttons === 0 && solve_index === -1 ?{iX:datum.iX, iY:datum.iY, iZ:datum.iZ, axis: (datum.iZ < cube_size - 1 && rotation_VER <= 180) || (datum.iZ !== 0 && rotation_VER > 180) ? 'z' : datum.axis} : selected"}, {"events":"@face:mouseout", "update":"cube_changing ? selected : null"}, {"events":"view:mouseup", "update":"null"} ] }, { "name":"perspective", "value":0.5, "bind":{"input":"range", "min": 0, "max": 2, "step": 0.05} } ], "scales":[ { "name":"color", "type":"ordinal", "domain":[1,2,3,4,5,6], "range":["darkorange","red","yellow","white","green","blue"] } ], "data":[ { "name":"points", "values":[{"iX":[]}], "transform":[ { "type":"formula", "expr":"[{iX:0,iY:0,iZ:0,axis:'z',face:1},{iX:0,iY:1,iZ:0,axis:'z',face:1},{iX:0,iY:2,iZ:0,axis:'z',face:1},{iX:1,iY:0,iZ:0,axis:'z',face:1},{iX:1,iY:1,iZ:0,axis:'z',face:1},{iX:1,iY:2,iZ:0,axis:'z',face:1},{iX:2,iY:0,iZ:0,axis:'z',face:1},{iX:2,iY:1,iZ:0,axis:'z',face:1},{iX:2,iY:2,iZ:0,axis:'z',face:1},{iX:0,iY:0,iZ:2,axis:'z',face:2},{iX:0,iY:1,iZ:2,axis:'z',face:2},{iX:0,iY:2,iZ:2,axis:'z',face:2},{iX:1,iY:0,iZ:2,axis:'z',face:2},{iX:1,iY:1,iZ:2,axis:'z',face:2},{iX:1,iY:2,iZ:2,axis:'z',face:2},{iX:2,iY:0,iZ:2,axis:'z',face:2},{iX:2,iY:1,iZ:2,axis:'z',face:2},{iX:2,iY:2,iZ:2,axis:'z',face:2},{iX:0,iY:0,iZ:0,axis:'x',face:3},{iX:0,iY:0,iZ:1,axis:'x',face:3},{iX:0,iY:0,iZ:2,axis:'x',face:3},{iX:0,iY:1,iZ:0,axis:'x',face:3},{iX:0,iY:1,iZ:1,axis:'x',face:3},{iX:0,iY:1,iZ:2,axis:'x',face:3},{iX:0,iY:2,iZ:0,axis:'x',face:3},{iX:0,iY:2,iZ:1,axis:'x',face:3},{iX:0,iY:2,iZ:2,axis:'x',face:3},{iX:2,iY:0,iZ:0,axis:'x',face:4},{iX:2,iY:0,iZ:1,axis:'x',face:4},{iX:2,iY:0,iZ:2,axis:'x',face:4},{iX:2,iY:1,iZ:0,axis:'x',face:4},{iX:2,iY:1,iZ:1,axis:'x',face:4},{iX:2,iY:1,iZ:2,axis:'x',face:4},{iX:2,iY:2,iZ:0,axis:'x',face:4},{iX:2,iY:2,iZ:1,axis:'x',face:4},{iX:2,iY:2,iZ:2,axis:'x',face:4},{iX:0,iY:0,iZ:0,axis:'y',face:5},{iX:0,iY:0,iZ:1,axis:'y',face:5},{iX:0,iY:0,iZ:2,axis:'y',face:5},{iX:1,iY:0,iZ:0,axis:'y',face:5},{iX:1,iY:0,iZ:1,axis:'y',face:5},{iX:1,iY:0,iZ:2,axis:'y',face:5},{iX:2,iY:0,iZ:0,axis:'y',face:5},{iX:2,iY:0,iZ:1,axis:'y',face:5},{iX:2,iY:0,iZ:2,axis:'y',face:5},{iX:0,iY:2,iZ:0,axis:'y',face:6},{iX:0,iY:2,iZ:1,axis:'y',face:6},{iX:0,iY:2,iZ:2,axis:'y',face:6},{iX:1,iY:2,iZ:0,axis:'y',face:6},{iX:1,iY:2,iZ:1,axis:'y',face:6},{iX:1,iY:2,iZ:2,axis:'y',face:6},{iX:2,iY:2,iZ:0,axis:'y',face:6},{iX:2,iY:2,iZ:1,axis:'y',face:6},{iX:2,iY:2,iZ:2,axis:'y',face:6}]", "as":"iX" }, { "type":"flatten", "fields":["iX"] }, { "type":"project", "fields":["iX.iX","iX.iY","iX.iZ","iX.axis","iX.face"], "as":["iX","iY","iZ","axis","face"] }, { "type":"formula", "expr":"datum.axis === 'x' ? {x:datum.iX===0?-1:1, y:0,z:0}: datum.axis === 'y' ? {x:0, y:datum.iY === 0 ? -1:1, z:0}: {x:0,y:0, z:datum.iZ ===0?-1:1}", "as":"normal" }, { "type":"formula", "expr":"datum.axis === 'x' ? {x:(datum.iX === cube_size - 1 ? cube_size : 0) - cube_size/2, y: (1/2 + datum.iY) - cube_size/2, z: (1/2 + datum.iZ) - cube_size/2}: datum.axis === 'y' ? {x:(1/2 + datum.iX)-cube_size/2, y: (datum.iY === cube_size - 1 ? cube_size:0) -cube_size/2, z:( 1/2 + datum.iZ)-cube_size/2} : {x:(1/2 + datum.iX)-cube_size/2, y: (1/2 + datum.iY)-cube_size/2, z: (datum.iZ === cube_size - 1 ? cube_size : 0)-cube_size/2}", "as":"center" }, { "type":"formula", "expr":"datum.axis === 'x' ? [{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2}] : datum.axis === 'y' ? 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[{x:datum.center.x - (1-cube_padding)/2 , y:datum.center.y, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y, z : datum.center.z - (1-cube_padding)/2}] : [{x:datum.center.x - (1-cube_padding)/2 , y:datum.center.y - (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z}]", "as":"points" }, { "type":"formula", "expr":"{x:(datum.iX+1/2) - cube_size/2, y: (1/2 + datum.iY) - cube_size/2, z: (1/2 + datum.iZ) - cube_size/2}", "as":"center" }, { "type":"flatten", "fields":["points"] } ] })32:Ta4a,({ "name":"projections", "source":"points", "transform":[ { "type":"formula", "expr":"{x:q.w * datum.normal.x + q.y*datum.normal.z- q.z * datum.normal.y, y:q.w * datum.normal.y - q.x * datum.normal.z + q.z*datum.normal.x, z:q.w * datum.normal.z + q.x*datum.normal.y - q.y * datum.normal.x, w: -q.x * datum.normal.x - q.y * datum.normal.y - q.z * datum.normal.z}", "as":"q1" }, { "type":"formula", "expr":"{z:datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w}", "as":"nq2" }, { "type":"filter", "expr":"datum.nq2.z>0" }, { "type":"formula", "expr":"{x:q.w * datum.center.x + q.y*datum.center.z- q.z * datum.center.y, y:q.w * datum.center.y - q.x * datum.center.z + q.z*datum.center.x, z:q.w * datum.center.z + q.x*datum.center.y - q.y * datum.center.x, w: -q.x * datum.center.x - q.y * datum.center.y - q.z * datum.center.z}", "as":"q1" }, { "type":"formula", "expr":"datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w", "as":"cq2_z" }, { "type":"collect", "sort":{"field":["cq2_z"]} }, { "type":"formula", "expr":"{x:q.w * datum.points.x + q.y*datum.points.z- q.z * datum.points.y, y:q.w * datum.points.y - q.x * datum.points.z + q.z*datum.points.x, z:q.w * datum.points.z + q.x*datum.points.y - q.y * datum.points.x, w: -q.x * datum.points.x - q.y * datum.points.y - q.z * datum.points.z}", "as":"q1" }, { "type":"formula", "expr":"{x:datum.q1.w * q_1.x + datum.q1.x * q_1.w + datum.q1.y * q_1.z - datum.q1.z * q_1.y, y:datum.q1.w * q_1.y - datum.q1.x * q_1.z + datum.q1.y * q_1.w + datum.q1.z * q_1.x, z:((datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w) - 1.5*sqrt(3))/(3*sqrt(3))}", "as":"pq2" }, { "type":"extent", "field":"pq2.z", "signal": "z_value" }, { "type":"formula", "expr":"(datum.pq2.x)*size*scale *(1+perspective)/(1 - perspective*datum.pq2.z) + width/2", "as":"x" }, { "type":"formula", "expr":"(datum.pq2.y)*size*scale *(1+perspective)/(1 - perspective*datum.pq2.z)+ height/2", "as":"y" }, { "type":"formula", "expr":"false", "as":"isProcessing" } ] })33:T443,md`## Adding perspective In the projections table there is a small difference that changes the rendering of the cube: perspective. In my other experiments, in order to simplify, I used orthographic projections. It means that I only cared about rotation of the camera and now about the distance between the points and the camera. When using perspective the far the object is from the camera, the smaller it should be. The good practice is to use a perspective matrix, configured with the field of view and the near and far planes. I simplified this to the minimum: the cube has a side of 3 units, it means that the radius of the sphere containing the cube is 3 multiply by square root of 3 (well, I hope so...). Substracting half of the radius to the z point and diving the result by the radius you'll have a z value variating between 0 and 1. Let's create now a variable named perspective that will vary from 0 (orthographic to 2). If you multiply the x and y paramters by (1+perspective)/(1-perspective*z), you will be able to configure the strength of the perspective effect. Here we go:`34:T2b32,spec = ({ "$schema": "https://vega.github.io/schema/vega/v5.json", "width":400, "height":400, "background":"black", "signals":[ { "name":"size", "init":"40*(min (width,height)/400)" }, { "name":"cube_padding", "value":0.02 }, { "name":"cube_size", "value":3 }, { "name":"scale", "value":1, "bind":{"input":"range","min": 0, "max": 2, "step": 0.1}, "on":[{"events":"view:mousewheel", "update":"max(0, min(2, scale + (event.wheelDelta > 0 ? 0.1 : -0.1)))"}] }, { "name":"angle_HOR", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_HOR + ((event.movementX < 0) ^ (rotation_VER > 180) ? 5 : (event.movementX > 0) ^(rotation_VER > 180) ? -5 : 0)"}] }, { "name":"validAngle_HOR", "update":"angle_HOR % 360 <0 ? 360 + angle_HOR % 360 : angle_HOR % 360" }, { "name":"angle_VER", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_VER + (event.movementY < 0 ? 5 : event.movementY > 0 ? -5 : 0)"}] }, { "name":"validAngle_VER", "update":"angle_VER % 360 <0 ? 360 + angle_VER % 360 : angle_VER % 360" }, { "name":"rotation_HOR", "value":45, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_HOR"}, "update":"validAngle_HOR"}] }, { "name":"rotation_VER", "value":65, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_VER"}, "update":"validAngle_VER"}] }, { "name":"qrAngle_HOR", "init":"PI*(rotation_HOR)/360", "on": [{"events":{"signal":"-rotation_HOR"}, "update":"PI*(rotation_HOR)/360"}] }, { "name":"qrAngle_VER", "init":"PI*(rotation_VER)/360", "on": [{"events":{"signal":"rotation_VER"}, "update":"PI*(rotation_VER)/360"}] }, { "name":"qrw0", "update":"cos(qrAngle_VER)" }, { "name":"qrw1", "update":"cos(qrAngle_HOR)" }, { "name":"qrx0", "update":"sin(qrAngle_VER)" }, { "name":"qrz1", "update":"sin(qrAngle_HOR)" }, { "name":"q", "update":"{x:qrx0*qrw1, y:-qrx0*qrz1, z:qrw0*qrz1, w: qrw0*qrw1}" }, { "name":"q_1", "update":"{x:-q.x, y:-q.y, z: -q.z, w: q.w}" }, { "name":"perspective", "value":0.5, "bind":{"input":"range", "min": 0, "max": 2, "step": 0.05} } ], "scales":[ { "name":"color", "type":"ordinal", "domain":[1,2,3,4,5,6], "range":["darkorange","red","yellow","white","green","blue"] } ], "data":[ { "name":"points", "values":[{"iX":[]}], "transform":[ { "type":"formula", "expr":"[{iX:0,iY:0,iZ:0,axis:'z',face:1},{iX:0,iY:1,iZ:0,axis:'z',face:1},{iX:0,iY:2,iZ:0,axis:'z',face:1},{iX:1,iY:0,iZ:0,axis:'z',face:1},{iX:1,iY:1,iZ:0,axis:'z',face:1},{iX:1,iY:2,iZ:0,axis:'z',face:1},{iX:2,iY:0,iZ:0,axis:'z',face:1},{iX:2,iY:1,iZ:0,axis:'z',face:1},{iX:2,iY:2,iZ:0,axis:'z',face:1},{iX:0,iY:0,iZ:2,axis:'z',face:2},{iX:0,iY:1,iZ:2,axis:'z',face:2},{iX:0,iY:2,iZ:2,axis:'z',face:2},{iX:1,iY:0,iZ:2,axis:'z',face:2},{iX:1,iY:1,iZ:2,axis:'z',face:2},{iX:1,iY:2,iZ:2,axis:'z',face:2},{iX:2,iY:0,iZ:2,axis:'z',face:2},{iX:2,iY:1,iZ:2,axis:'z',face:2},{iX:2,iY:2,iZ:2,axis:'z',face:2},{iX:0,iY:0,iZ:0,axis:'x',face:3},{iX:0,iY:0,iZ:1,axis:'x',face:3},{iX:0,iY:0,iZ:2,axis:'x',face:3},{iX:0,iY:1,iZ:0,axis:'x',face:3},{iX:0,iY:1,iZ:1,axis:'x',face:3},{iX:0,iY:1,iZ:2,axis:'x',face:3},{iX:0,iY:2,iZ:0,axis:'x',face:3},{iX:0,iY:2,iZ:1,axis:'x',face:3},{iX:0,iY:2,iZ:2,axis:'x',face:3},{iX:2,iY:0,iZ:0,axis:'x',face:4},{iX:2,iY:0,iZ:1,axis:'x',face:4},{iX:2,iY:0,iZ:2,axis:'x',face:4},{iX:2,iY:1,iZ:0,axis:'x',face:4},{iX:2,iY:1,iZ:1,axis:'x',face:4},{iX:2,iY:1,iZ:2,axis:'x',face:4},{iX:2,iY:2,iZ:0,axis:'x',face:4},{iX:2,iY:2,iZ:1,axis:'x',face:4},{iX:2,iY:2,iZ:2,axis:'x',face:4},{iX:0,iY:0,iZ:0,axis:'y',face:5},{iX:0,iY:0,iZ:1,axis:'y',face:5},{iX:0,iY:0,iZ:2,axis:'y',face:5},{iX:1,iY:0,iZ:0,axis:'y',face:5},{iX:1,iY:0,iZ:1,axis:'y',face:5},{iX:1,iY:0,iZ:2,axis:'y',face:5},{iX:2,iY:0,iZ:0,axis:'y',face:5},{iX:2,iY:0,iZ:1,axis:'y',face:5},{iX:2,iY:0,iZ:2,axis:'y',face:5},{iX:0,iY:2,iZ:0,axis:'y',face:6},{iX:0,iY:2,iZ:1,axis:'y',face:6},{iX:0,iY:2,iZ:2,axis:'y',face:6},{iX:1,iY:2,iZ:0,axis:'y',face:6},{iX:1,iY:2,iZ:1,axis:'y',face:6},{iX:1,iY:2,iZ:2,axis:'y',face:6},{iX:2,iY:2,iZ:0,axis:'y',face:6},{iX:2,iY:2,iZ:1,axis:'y',face:6},{iX:2,iY:2,iZ:2,axis:'y',face:6}]", "as":"iX" }, { "type":"flatten", "fields":["iX"] }, { "type":"project", "fields":["iX.iX","iX.iY","iX.iZ","iX.axis","iX.face"], "as":["iX","iY","iZ","axis","face"] }, { "type":"formula", "expr":"datum.axis === 'x' ? 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[{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2}] : datum.axis === 'y' ? [{x:datum.center.x - (1-cube_padding)/2 , y:datum.center.y, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y, z : datum.center.z - (1-cube_padding)/2}] : [{x:datum.center.x - (1-cube_padding)/2 , y:datum.center.y - (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z}]", "as":"points" }, { "type":"formula", "expr":"{x:(datum.iX+1/2) - cube_size/2, y: (1/2 + datum.iY) - cube_size/2, z: (1/2 + datum.iZ) - cube_size/2}", "as":"center" }, { "type":"flatten", "fields":["points"] } ] }, { "name":"projections", "source":"points", "transform":[ { "type":"formula", "expr":"{x:q.w * datum.normal.x + q.y*datum.normal.z- q.z * datum.normal.y, y:q.w * datum.normal.y - q.x * datum.normal.z + q.z*datum.normal.x, z:q.w * datum.normal.z + q.x*datum.normal.y - q.y * datum.normal.x, w: -q.x * datum.normal.x - q.y * datum.normal.y - q.z * datum.normal.z}", "as":"q1" }, { "type":"formula", "expr":"{z:datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w}", "as":"nq2" }, { "type":"filter", "expr":"datum.nq2.z>0" }, { "type":"formula", "expr":"{x:q.w * datum.center.x + q.y*datum.center.z- q.z * datum.center.y, y:q.w * datum.center.y - q.x * datum.center.z + q.z*datum.center.x, z:q.w * datum.center.z + q.x*datum.center.y - q.y * datum.center.x, w: -q.x * datum.center.x - q.y * datum.center.y - q.z * datum.center.z}", "as":"q1" }, { "type":"formula", "expr":"datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w", "as":"cq2_z" }, { "type":"collect", "sort":{"field":["cq2_z"]} }, { "type":"formula", "expr":"{x:q.w * datum.points.x + q.y*datum.points.z- q.z * datum.points.y, y:q.w * datum.points.y - q.x * datum.points.z + q.z*datum.points.x, z:q.w * datum.points.z + q.x*datum.points.y - q.y * datum.points.x, w: -q.x * datum.points.x - q.y * datum.points.y - q.z * datum.points.z}", "as":"q1" }, { "type":"formula", "expr":"{x:datum.q1.w * q_1.x + datum.q1.x * q_1.w + datum.q1.y * q_1.z - datum.q1.z * q_1.y, y:datum.q1.w * q_1.y - datum.q1.x * q_1.z + datum.q1.y * q_1.w + datum.q1.z * q_1.x, z:((datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w) - 1.5*sqrt(3))/(3*sqrt(3))}", "as":"pq2" }, { "type":"extent", "field":"pq2.z", "signal": "z_value" }, { "type":"formula", "expr":"(datum.pq2.x)*size*scale *(1+perspective)/(1 - perspective*datum.pq2.z) + width/2", "as":"x" }, { "type":"formula", "expr":"(datum.pq2.y)*size*scale *(1+perspective)/(1 - perspective*datum.pq2.z)+ height/2", "as":"y" }, { "type":"formula", "expr":"false", "as":"isProcessing" } ] } ], "marks":[ { "type": "group", "from": { "facet": { "name": "area", "data": "projections", "groupby": [ "iX", "iY", "iZ", "face", "cq2_z" ] } }, "marks": [ { "type": "line", "name":"face", "from": { "data": "area" }, "encode": { "update": { "x": { "field": "x" }, "y": { "field": "y" }, "y2": { "value": 0 }, "fill": [{ "field": "face", "scale": "color" }], "strokeWidth":[{"value":1}], "stroke":[{"value":"black"}] } } } ] } ] })35:T687,md`**NOTES:** - Most of the signals are exactly the same as previous 3D experiments and won't be detailed here - You can see the projections formula in the x an y formula at the end of the projections table - I reverted the cube rotation when rotation_VER is between 180 and 360: this because once the cube will be mixed, you won't know what is the top or bottom face and it become confusing - When raising up the perspective factor, you'll notice some clipping issues (areas that should be hidden, that are drawn over areas that shouldn't be hidden): this is because the areas are grouped by face when rendering so the z axis faces will be drawn first, then the x axis faces and finally the y axis faces. Life being too short, that issue won't be solved in that experiment ## Manipulating the cube Now that we have our game platform, we need to be able to interact with it. That part seemed challenging at first glance, but is in fact quite easy and straight forward. For the moment, we ha ve one table containing the points definitions and another that project them on the screen after applying rotation and perspective. We want a third table taking from points and serving projections. We will also create a new quaternion representing a modification of the cube. That quaternion will be used to modify the points of our intermediary table. Not all points: We need to be able to select: one axis to rotate and one index of rotation (you have 3 possibilities per axis). ### Selecting We will first focus on the selection part: - We add 2 signals \`\`selected\`\` and \`\`cube_changing\`\`:`36:T2f8c,embed({ "$schema": "https://vega.github.io/schema/vega/v5.json", "width":400, "height":400, "background":"black", "signals":[ { "name":"size", "init":"40*(min (width,height)/400)" }, { "name":"cube_padding", "value":0.02 }, { "name":"cube_size", "value":3 }, { "name":"scale", "value":1, "bind":{"input":"range","min": 0, "max": 2, "step": 0.1}, "on":[{"events":"view:mousewheel", "update":"max(0, min(2, scale + (event.wheelDelta > 0 ? 0.1 : -0.1)))"}] }, { "name":"angle_HOR", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_HOR + (cube_changing ? 0 : ((event.movementX < 0) ^ (rotation_VER > 180) ? 5 : (event.movementX > 0) ^(rotation_VER > 180) ? -5 : 0))"}] }, { "name":"validAngle_HOR", "update":"angle_HOR % 360 <0 ? 360 + angle_HOR % 360 : angle_HOR % 360" }, { "name":"angle_VER", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_VER + ( cube_changing ? 0 :(event.movementY < 0 ? 5 : event.movementY > 0 ? -5 : 0))"}] }, { "name":"validAngle_VER", "update":"angle_VER % 360 <0 ? 360 + angle_VER % 360 : angle_VER % 360" }, { "name":"rotation_HOR", "value":45, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_HOR"}, "update":"validAngle_HOR"}] }, { "name":"rotation_VER", "value":65, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_VER"}, "update":"validAngle_VER"}] }, { "name":"qrAngle_HOR", "init":"PI*(rotation_HOR)/360", "on": [{"events":{"signal":"-rotation_HOR"}, "update":"PI*(rotation_HOR)/360"}] }, { "name":"qrAngle_VER", "init":"PI*(rotation_VER)/360", "on": [{"events":{"signal":"rotation_VER"}, "update":"PI*(rotation_VER)/360"}] }, { "name":"qrw0", "update":"cos(qrAngle_VER)" }, { "name":"qrw1", "update":"cos(qrAngle_HOR)" }, { "name":"qrx0", "update":"sin(qrAngle_VER)" }, { "name":"qrz1", "update":"sin(qrAngle_HOR)" }, { "name":"q", "update":"{x:qrx0*qrw1, y:-qrx0*qrz1, z:qrw0*qrz1, w: qrw0*qrw1}" }, { "name":"q_1", "update":"{x:-q.x, y:-q.y, z: -q.z, w: q.w}" }, { "name":"perspective", "value":0.5, "bind":{"input":"range", "min": 0, "max": 2, "step": 0.05} }, { "name":"cube_changing", "init":"false", "on":[{"events":"view:mousedown", "update":"selected!=null"},{"events":"view:mouseup", "update":"false"}] }, { "name":"selected", "init":"null", "on":[ {"events":"@face:mousemove", "update":"event.buttons === 0 ?{iX:datum.iX, iY:datum.iY, iZ:datum.iZ, axis: (datum.iZ < cube_size - 1 && rotation_VER <= 180) || (datum.iZ !== 0 && rotation_VER > 180) ? 'z' : datum.axis} : selected"}, {"events":"@face:mouseout", "update":"cube_changing ? selected : null"}, {"events":"view:mouseup", "update":"null"} ] } ], "scales":[ { "name":"color", "type":"ordinal", "domain":[1,2,3,4,5,6], "range":["darkorange","red","yellow","white","green","blue"] } ], "data":[ { "name":"points", "values":[{"iX":[]}], "transform":[ { "type":"formula", "expr":"[{iX:0,iY:0,iZ:0,axis:'z',face:1},{iX:0,iY:1,iZ:0,axis:'z',face:1},{iX:0,iY:2,iZ:0,axis:'z',face:1},{iX:1,iY:0,iZ:0,axis:'z',face:1},{iX:1,iY:1,iZ:0,axis:'z',face:1},{iX:1,iY:2,iZ:0,axis:'z',face:1},{iX:2,iY:0,iZ:0,axis:'z',face:1},{iX:2,iY:1,iZ:0,axis:'z',face:1},{iX:2,iY:2,iZ:0,axis:'z',face:1},{iX:0,iY:0,iZ:2,axis:'z',face:2},{iX:0,iY:1,iZ:2,axis:'z',face:2},{iX:0,iY:2,iZ:2,axis:'z',face:2},{iX:1,iY:0,iZ:2,axis:'z',face:2},{iX:1,iY:1,iZ:2,axis:'z',face:2},{iX:1,iY:2,iZ:2,axis:'z',face:2},{iX:2,iY:0,iZ:2,axis:'z',face:2},{iX:2,iY:1,iZ:2,axis:'z',face:2},{iX:2,iY:2,iZ:2,axis:'z',face:2},{iX:0,iY:0,iZ:0,axis:'x',face:3},{iX:0,iY:0,iZ:1,axis:'x',face:3},{iX:0,iY:0,iZ:2,axis:'x',face:3},{iX:0,iY:1,iZ:0,axis:'x',face:3},{iX:0,iY:1,iZ:1,axis:'x',face:3},{iX:0,iY:1,iZ:2,axis:'x',face:3},{iX:0,iY:2,iZ:0,axis:'x',face:3},{iX:0,iY:2,iZ:1,axis:'x',face:3},{iX:0,iY:2,iZ:2,axis:'x',face:3},{iX:2,iY:0,iZ:0,axis:'x',face:4},{iX:2,iY:0,iZ:1,axis:'x',face:4},{iX:2,iY:0,iZ:2,axis:'x',face:4},{iX:2,iY:1,iZ:0,axis:'x',face:4},{iX:2,iY:1,iZ:1,axis:'x',face:4},{iX:2,iY:1,iZ:2,axis:'x',face:4},{iX:2,iY:2,iZ:0,axis:'x',face:4},{iX:2,iY:2,iZ:1,axis:'x',face:4},{iX:2,iY:2,iZ:2,axis:'x',face:4},{iX:0,iY:0,iZ:0,axis:'y',face:5},{iX:0,iY:0,iZ:1,axis:'y',face:5},{iX:0,iY:0,iZ:2,axis:'y',face:5},{iX:1,iY:0,iZ:0,axis:'y',face:5},{iX:1,iY:0,iZ:1,axis:'y',face:5},{iX:1,iY:0,iZ:2,axis:'y',face:5},{iX:2,iY:0,iZ:0,axis:'y',face:5},{iX:2,iY:0,iZ:1,axis:'y',face:5},{iX:2,iY:0,iZ:2,axis:'y',face:5},{iX:0,iY:2,iZ:0,axis:'y',face:6},{iX:0,iY:2,iZ:1,axis:'y',face:6},{iX:0,iY:2,iZ:2,axis:'y',face:6},{iX:1,iY:2,iZ:0,axis:'y',face:6},{iX:1,iY:2,iZ:1,axis:'y',face:6},{iX:1,iY:2,iZ:2,axis:'y',face:6},{iX:2,iY:2,iZ:0,axis:'y',face:6},{iX:2,iY:2,iZ:1,axis:'y',face:6},{iX:2,iY:2,iZ:2,axis:'y',face:6}]", "as":"iX" }, { "type":"flatten", "fields":["iX"] }, { "type":"project", "fields":["iX.iX","iX.iY","iX.iZ","iX.axis","iX.face"], "as":["iX","iY","iZ","axis","face"] }, { "type":"formula", "expr":"datum.axis === 'x' ? {x:datum.iX===0?-1:1, y:0,z:0}: datum.axis === 'y' ? {x:0, y:datum.iY === 0 ? -1:1, z:0}: {x:0,y:0, z:datum.iZ ===0?-1:1}", "as":"normal" }, { "type":"formula", "expr":"datum.axis === 'x' ? {x:(datum.iX === cube_size - 1 ? cube_size : 0) - cube_size/2, y: (1/2 + datum.iY) - cube_size/2, z: (1/2 + datum.iZ) - cube_size/2}: datum.axis === 'y' ? {x:(1/2 + datum.iX)-cube_size/2, y: (datum.iY === cube_size - 1 ? cube_size:0) -cube_size/2, z:( 1/2 + datum.iZ)-cube_size/2} : {x:(1/2 + datum.iX)-cube_size/2, y: (1/2 + datum.iY)-cube_size/2, z: (datum.iZ === cube_size - 1 ? cube_size : 0)-cube_size/2}", "as":"center" }, { "type":"formula", "expr":"datum.axis === 'x' ? 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[{x:datum.center.x - (1-cube_padding)/2 , y:datum.center.y, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y, z : datum.center.z - (1-cube_padding)/2}] : [{x:datum.center.x - (1-cube_padding)/2 , y:datum.center.y - (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z}]", "as":"points" }, { "type":"formula", "expr":"{x:(datum.iX+1/2) - cube_size/2, y: (1/2 + datum.iY) - cube_size/2, z: (1/2 + datum.iZ) - cube_size/2}", "as":"center" }, { "type":"flatten", "fields":["points"] } ] }, { "name":"projections", "source":"points", "transform":[ { "type":"formula", "expr":"{x:q.w * datum.normal.x + q.y*datum.normal.z- q.z * datum.normal.y, y:q.w * datum.normal.y - q.x * datum.normal.z + q.z*datum.normal.x, z:q.w * datum.normal.z + q.x*datum.normal.y - q.y * datum.normal.x, w: -q.x * datum.normal.x - q.y * datum.normal.y - q.z * datum.normal.z}", "as":"q1" }, { "type":"formula", "expr":"{z:datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w}", "as":"nq2" }, { "type":"filter", "expr":"datum.nq2.z>0" }, { "type":"formula", "expr":"{x:q.w * datum.center.x + q.y*datum.center.z- q.z * datum.center.y, y:q.w * datum.center.y - q.x * datum.center.z + q.z*datum.center.x, z:q.w * datum.center.z + q.x*datum.center.y - q.y * datum.center.x, w: -q.x * datum.center.x - q.y * datum.center.y - q.z * datum.center.z}", "as":"q1" }, { "type":"formula", "expr":"datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w", "as":"cq2_z" }, { "type":"collect", "sort":{"field":["cq2_z"]} }, { "type":"formula", "expr":"{x:q.w * datum.points.x + q.y*datum.points.z- q.z * datum.points.y, y:q.w * datum.points.y - q.x * datum.points.z + q.z*datum.points.x, z:q.w * datum.points.z + q.x*datum.points.y - q.y * datum.points.x, w: -q.x * datum.points.x - q.y * datum.points.y - q.z * datum.points.z}", "as":"q1" }, { "type":"formula", "expr":"{x:datum.q1.w * q_1.x + datum.q1.x * q_1.w + datum.q1.y * q_1.z - datum.q1.z * q_1.y, y:datum.q1.w * q_1.y - datum.q1.x * q_1.z + datum.q1.y * q_1.w + datum.q1.z * q_1.x, z:((datum.q1.w * q_1.z + datum.q1.x * q_1.y - datum.q1.y * q_1.x + datum.q1.z * q_1.w) - 1.5*sqrt(3))/(3*sqrt(3))}", "as":"pq2" }, { "type":"extent", "field":"pq2.z", "signal": "z_value" }, { "type":"formula", "expr":"(datum.pq2.x)*size*scale *(1+perspective)/(1 - perspective*datum.pq2.z) + width/2", "as":"x" }, { "type":"formula", "expr":"(datum.pq2.y)*size*scale *(1+perspective)/(1 - perspective*datum.pq2.z)+ height/2", "as":"y" }, { "type":"formula", "expr":"false", "as":"isProcessing" } ] } ], "marks":[ { "type": "group", "from": { "facet": { "name": "area", "data": "projections", "groupby": [ "iX", "iY", "iZ", "face", "cq2_z" ] } }, "marks": [ { "type": "line", "name":"face", "from": { "data": "area" }, "encode": { "update": { "x": { "field": "x" }, "y": { "field": "y" }, "y2": { "value": 0 }, "fill": [{ "field": "face", "scale": "color" }], "strokeWidth":[{"test":"selected !== null && ((selected.axis === 'x' && datum.iY === selected.iY) || (selected.axis === 'y' && datum.iX === selected.iX) || (selected.axis === 'z' && datum.iZ === selected.iZ))", "value":3},{"value":1}], "stroke":[{"test":"selected !== null && ((selected.axis === 'x' && datum.iY === selected.iY) || (selected.axis === 'y' && datum.iX === selected.iX) || (selected.axis === 'z' && datum.iZ === selected.iZ))", "value":"steelblue"},{"value":"black"}] } } } ] } ] },{"renderer":"svg"})37:T6e9,([{ "name":"angle_Line", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "force": true,"update":"rotation_Line.angle === 0 && selected !=null ? ((selected.axis === 'z' ? (event.movementX < 0 ^ (rotation_VER > 180) ? 1 : event.movementX === 0 ? 0 : -1) : (selected.axis === 'x' ? (event.movementY < 0 ^ isYZBack ^ (rotation_VER > 180) ? 1 : event.movementY === 0 ? 0 : -1) : (selected.axis === 'y' ? (event.movementY < 0 ^ isXZBack ^ (rotation_VER > 180) ? 1 : event.movementY === 0 ? 0 : -1) : 0)))*10) : 0"}] }, { "name":"rotation_Line", "value":{"angle":0, "axis":null, "iX":-1, "iY":-1, "iZ":-1}, "on":[{"events":{"signal":"angle_Line"}, "update":"selected !== null ? {angle:angle_Line, axis : selected.axis, iX: selected.iX, iY:selected.iY, iZ:selected.iZ}: {angle:0, axis:null, iX:-1, iY:-1, iZ:-1}"}] }, { "name":"qrAngle_Line", "init":"PI*(rotation_Line.angle)/360", "on": [{"events":{"signal":"rotation_Line"}, "update":"PI*(rotation_Line.angle)/360"}] }, { "name":"qLine", "update":"{x: (rotation_Line.axis === 'y' ? sin(qrAngle_Line) : 0), y:(rotation_Line.axis === 'x' ? sin(-qrAngle_Line) : 0), z:(rotation_Line.axis === 'z' ? sin(qrAngle_Line) : 0), w : (rotation_Line.axis !==null ? cos(qrAngle_Line) : 1)}" }, { "name":"qLine_1", "update":"{x: -qLine.x, y: -qLine.y, z: -qLine.z, w: qLine.w}" }, { "name":"isYZBack", "update":"{z: 2*(q.x * q.z) - 2*(q.w * q.y)}.z < 0" }, { "name":"isXZBack", "update":"{z: 2*(q.y * q.z) + 2 *(q.w * q.x)}.z < 0" }, { "name":"isXYBack", "update":"{z: (q.z*q.z) - (q.y*q.y) - (q.x*q.x) + (q.w*q.w)}.z < 0" }])38:T42f,md`- angle_Line is receiving the angle from the mouse move. The difference with the camera rotation is that we want to increase or decrease an existing value. The trick I used: If the rotation_Line angle is 0 is setting to a value to 10 or -10 according to the direction. If the angle is not 0 is setting the angle to 0. The quaternion will receive 0 then 10 or -10 the 0. And the points will be rotated from 10 to 10 - rotation_Line is creating a rotation object according to angle_line - qrAngle_Line is the rotation_angle in radians - qLine and qLine_1 are the line rotation quaternion and inverted. The quaternion parameters are changing accordingly to the rotation axis - isYZBack, isXZBack and isXYBack are telling if a face of a specific axis is backside. This is used to revert the angle of rotation accordingly to the position of the cube to have a uniform behavior Now we can add the points_dyn table tha will apply the line transformations:`39:T1260,({ "name":"points_dyn", "source":"points", "transform":[ { "type":"formula", "expr":"(rotation_Line.angle !== 0 && rotation_Line.axis !== null && ((rotation_Line.axis === 'x' && datum.iY === rotation_Line.iY) || (rotation_Line.axis === 'y' && datum.iX === rotation_Line.iX) || (rotation_Line.axis === 'z' && datum.iZ === rotation_Line.iZ)))", "as":"isTransformed" }, { "type":"formula", "expr":"datum.isTransformed?{x:qLine.w * datum.normal.x + qLine.y*datum.normal.z- qLine.z * datum.normal.y, y:qLine.w * datum.normal.y - qLine.x * datum.normal.z + qLine.z*datum.normal.x, z:qLine.w * datum.normal.z + qLine.x*datum.normal.y - qLine.y * datum.normal.x, w: -qLine.x * datum.normal.x - qLine.y * datum.normal.y - qLine.z * datum.normal.z}:{}", "as":"q1" }, { "type":"formula", "expr":"datum.isTransformed?{x:datum.q1.w * qLine_1.x + datum.q1.x * qLine_1.w + datum.q1.y * qLine_1.z - datum.q1.z * qLine_1.y, y:datum.q1.w * qLine_1.y - datum.q1.x * qLine_1.z + datum.q1.y * qLine_1.w + datum.q1.z * qLine_1.x,z:datum.q1.w * qLine_1.z + datum.q1.x * qLine_1.y - datum.q1.y * qLine_1.x + datum.q1.z * qLine_1.w}:datum.normal", "as":"normal" }, { "type":"formula", "expr":"datum.isTransformed?{x:qLine.w * datum.center.x + qLine.y*datum.center.z- qLine.z * datum.center.y, y:qLine.w * datum.center.y - qLine.x * datum.center.z + qLine.z*datum.center.x, z:qLine.w * datum.center.z + qLine.x*datum.center.y - qLine.y * datum.center.x, w: -qLine.x * datum.center.x - qLine.y * datum.center.y - qLine.z * datum.center.z}: {}", "as":"q1" }, { "type":"formula", "expr":"datum.isTransformed?{x:datum.q1.w * qLine_1.x + datum.q1.x * qLine_1.w + datum.q1.y * qLine_1.z - datum.q1.z * qLine_1.y, y:datum.q1.w * qLine_1.y - datum.q1.x * qLine_1.z + datum.q1.y * qLine_1.w + datum.q1.z * qLine_1.x,z:datum.q1.w * qLine_1.z + datum.q1.x * qLine_1.y - datum.q1.y * qLine_1.x + datum.q1.z * qLine_1.w}: datum.center", "as":"center" }, { "type":"formula", "expr":"datum.isTransformed?{x:qLine.w * datum.points.x + qLine.y*datum.points.z- qLine.z * datum.points.y, y:qLine.w * datum.points.y - qLine.x * datum.points.z + qLine.z*datum.points.x, z:qLine.w * datum.points.z + qLine.x*datum.points.y - qLine.y * datum.points.x, w: -qLine.x * datum.points.x - qLine.y * datum.points.y - qLine.z * datum.points.z}:{}", "as":"q1" }, { "type":"formula", "expr":"datum.isTransformed?{x:datum.q1.w * qLine_1.x + datum.q1.x * qLine_1.w + datum.q1.y * qLine_1.z - datum.q1.z * qLine_1.y, y:datum.q1.w * qLine_1.y - datum.q1.x * qLine_1.z + datum.q1.y * qLine_1.w + datum.q1.z * qLine_1.x,z:datum.q1.w * qLine_1.z + datum.q1.x * qLine_1.y - datum.q1.y * qLine_1.x + datum.q1.z * qLine_1.w}:datum.points", "as":"points" }, { "type":"formula", "expr":"datum.isTransformed ? {r:rotation_Line.axis, a: ((isDefined(datum.rotation) ? datum.rotation.a: 0) + rotation_Line.angle)} : datum.rotation", "as":"rotation" }, { "type":"formula", "expr":"!cube_changing && isValid(datum.rotation) && datum.rotation.a!==0", "as":"isUpdated" }, { "type":"formula", "expr":"datum.isUpdated && datum.rotation.a % 90 === 0 ? (datum.rotation.a % 180 === 0 ? datum.axis : (datum.rotation.r === 'x' && datum.axis !== 'y') ? (datum.axis !== 'z'?'z':'x'): (datum.rotation.r === 'y' && datum.axis !== 'x') ? (datum.axis !== 'z'?'z':'y'): (datum.rotation.r === 'z' && datum.axis !== 'z') ? (datum.axis!=='y'?'y':'x') : datum.axis) : datum.axis", "as":"axis" }, { "type":"formula", "expr":"datum.isUpdated && datum.rotation.a % 90 === 0 ? round(datum.center.x) < 0 ? 0 : round(datum.center.x)> 0 ? 2 : 1 : datum.iX", "as":"iX" }, { "type":"formula", "expr":"datum.isUpdated && datum.rotation.a % 90 === 0 ? round(datum.center.y) < 0 ? 0 : round(datum.center.y)> 0 ? 2 : 1 : datum.iY", "as":"iY" }, { "type":"formula", "expr":"datum.isUpdated && datum.rotation.a % 90 === 0 ? round(datum.center.z) < 0 ? 0 : round(datum.center.z)> 0 ? 2 : 1 : datum.iZ", "as":"iZ" }, { "type":"formula", "expr":"datum.isUpdated && datum.rotation.a % 90 === 0 ? {a:0} : datum.rotation", "as":"rotation" } ] })3a:T56b,md` - The first (0) tranform check which points will be transformed the rotation_Line object as reference for the selection - Transform 1 to 6 are transforming the normal, the center and the point only for the transofrmed points - Transform 7 is updating the rotation applied to a line during one drag - Transform 8 is checking if the rotation is finished and has a change. This will trigger the data table when the user stop to drag a line and perform some extra actions only at that moment - Transform 9 to 12 are updating the cube index only if a rotation is a multiple of an angle of 90 degrees. If we don't do that the selection algorithm won't work for the next transformation - Transform 13 reset the rotation information if the angle of rotation was a multiple of 90 degrees. This will allow to know if a rotation was completed or not (used later) **NOTE**: Update the new position of the cube is crucial. I used the following algorithm: after to have rotated the center, knowing the the cube mesures 3 units we can tell the new index rounding the value of the center. If it's negative this is the back side, if positive this is the front side, otherwise the middle side. We also need to update the new axis of each face. This done checking the rotation axis. When rotating on z by example, the axis will switch from x to y every 90 degrees. And here's the transformation test:`3b:T4f1e,embed({ "$schema": "https://vega.github.io/schema/vega/v5.json", "width":400, "height":400, "background":"black", "signals":[ { "name":"size", "init":"40*(min (width,height)/400)" }, { "name":"cube_padding", "value":0.02 }, { "name":"cube_size", "value":3 }, { "name":"btn_reset_pressed", "on":[{"events":"@btn_reset:mousedown,@txt_reset:mousedown", "update":"true"}, {"events":"@btn_reset:mouseup,@txt_reset:mouseup", "update":"false"}] }, { "name":"reset", "on": [{"events":"@btn_reset:mousedown,@txt_reset:mousedown", "update":"setdata('points',[{iX:[]}])"}, {"events":"@btn_reset:mouseup,@txt_reset:mouseup", "update":"0"}] }, { "name":"scale", "value":1, "bind":{"input":"range","min": 0, "max": 2, "step": 0.1}, "on":[{"events":"view:mousewheel", "update":"max(0, min(2, scale + (event.wheelDelta > 0 ? 0.1 : -0.1)))"}] }, { "name":"angle_HOR", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_HOR + (cube_changing ? 0 : ((event.movementX < 0) ^ (rotation_VER > 180) ? 5 : (event.movementX > 0) ^(rotation_VER > 180) ? -5 : 0))"}] }, { "name":"validAngle_HOR", "update":"angle_HOR % 360 <0 ? 360 + angle_HOR % 360 : angle_HOR % 360" }, { "name":"angle_VER", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_VER + ( cube_changing ? 0 :(event.movementY < 0 ? 5 : event.movementY > 0 ? -5 : 0))"}] }, { "name":"angle_Line", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "force": true,"update":"rotation_Line.angle === 0 && selected !=null ? ((selected.axis === 'z' ? (event.movementX < 0 ^ (rotation_VER > 180) ? 1 : event.movementX === 0 ? 0 : -1) : (selected.axis === 'x' ? (event.movementY < 0 ^ isYZBack ^ (rotation_VER > 180) ? 1 : event.movementY === 0 ? 0 : -1) : (selected.axis === 'y' ? (event.movementY < 0 ^ isXZBack ^ (rotation_VER > 180) ? 1 : event.movementY === 0 ? 0 : -1) : 0)))*10) : 0"}] }, { "name":"validAngle_VER", "update":"angle_VER % 360 <0 ? 360 + angle_VER % 360 : angle_VER % 360" }, { "name":"rotation_HOR", "value":45, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_HOR"}, "update":"validAngle_HOR"}] }, { "name":"rotation_VER", "value":65, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_VER"}, "update":"validAngle_VER"}] }, { "name":"rotation_Line", "value":{"angle":0, "axis":null, "iX":-1, "iY":-1, "iZ":-1}, "on":[{"events":{"signal":"angle_Line"}, "update":"selected !== null ? {angle:angle_Line, axis : selected.axis, iX: selected.iX, iY:selected.iY, iZ:selected.iZ}: {angle:0, axis:null, iX:-1, iY:-1, iZ:-1}"}] }, { "name":"qrAngle_HOR", "init":"PI*(rotation_HOR)/360", "on": [{"events":{"signal":"-rotation_HOR"}, "update":"PI*(rotation_HOR)/360"}] }, { "name":"qrAngle_VER", "init":"PI*(rotation_VER)/360", "on": [{"events":{"signal":"rotation_VER"}, "update":"PI*(rotation_VER)/360"}] }, { "name":"qrAngle_Line", "init":"PI*(rotation_Line.angle)/360", "on": [{"events":{"signal":"rotation_Line"}, "update":"PI*(rotation_Line.angle)/360"}] }, { "name":"qrw0", "update":"cos(qrAngle_VER)" }, { "name":"qrw1", "update":"cos(qrAngle_HOR)" }, { "name":"qrx0", "update":"sin(qrAngle_VER)" }, { "name":"qrz1", "update":"sin(qrAngle_HOR)" }, { "name":"q", "update":"{x:qrx0*qrw1, y:-qrx0*qrz1, z:qrw0*qrz1, w: qrw0*qrw1}" }, { "name":"q_1", "update":"{x:-q.x, y:-q.y, z: -q.z, w: q.w}" }, { "name":"qLine", "update":"{x: (rotation_Line.axis === 'y' ? sin(qrAngle_Line) : 0), y:(rotation_Line.axis === 'x' ? sin(-qrAngle_Line) : 0), z:(rotation_Line.axis === 'z' ? sin(qrAngle_Line) : 0), w : (rotation_Line.axis !==null ? cos(qrAngle_Line) : 1)}" }, { "name":"qLine_1", "update":"{x: -qLine.x, y: -qLine.y, z: -qLine.z, w: qLine.w}" }, { "name":"isYZBack", "update":"{z: 2*(q.x * q.z) - 2*(q.w * q.y)}.z < 0" }, { "name":"isXZBack", "update":"{z: 2*(q.y * q.z) + 2 *(q.w * q.x)}.z < 0" }, { "name":"isXYBack", "update":"{z: (q.z*q.z) - (q.y*q.y) - (q.x*q.x) + (q.w*q.w)}.z < 0" }, { "name":"perspective", "value":0.5, "bind":{"input":"range", "min": 0, "max": 2, "step": 0.05} }, { "name":"cube_changing", "init":"false", "on":[{"events":"view:mousedown", "update":"selected!=null"},{"events":"view:mouseup", "update":"false"}] }, { "name":"selected", "init":"null", "on":[ {"events":"@face:mousemove", "update":"event.buttons === 0 ?{iX:datum.iX, iY:datum.iY, iZ:datum.iZ, axis: (datum.iZ < cube_size - 1 && rotation_VER <= 180) || (datum.iZ !== 0 && rotation_VER > 180) ? 'z' : datum.axis} : selected"}, {"events":"@face:mouseout", "update":"cube_changing ? selected : null"}, {"events":"view:mouseup", "update":"null"} ] } ], "scales":[ { "name":"color", "type":"ordinal", "domain":[1,2,3,4,5,6], "range":["darkorange","red","yellow","white","green","blue"] } ], "data":[ { "name":"points", "values":[{"iX":[]}], "transform":[ { "type":"formula", "expr":"[{iX:0,iY:0,iZ:0,axis:'z',face:1},{iX:0,iY:1,iZ:0,axis:'z',face:1},{iX:0,iY:2,iZ:0,axis:'z',face:1},{iX:1,iY:0,iZ:0,axis:'z',face:1},{iX:1,iY:1,iZ:0,axis:'z',face:1},{iX:1,iY:2,iZ:0,axis:'z',face:1},{iX:2,iY:0,iZ:0,axis:'z',face:1},{iX:2,iY:1,iZ:0,axis:'z',face:1},{iX:2,iY:2,iZ:0,axis:'z',face:1},{iX:0,iY:0,iZ:2,axis:'z',face:2},{iX:0,iY:1,iZ:2,axis:'z',face:2},{iX:0,iY:2,iZ:2,axis:'z',face:2},{iX:1,iY:0,iZ:2,axis:'z',face:2},{iX:1,iY:1,iZ:2,axis:'z',face:2},{iX:1,iY:2,iZ:2,axis:'z',face:2},{iX:2,iY:0,iZ:2,axis:'z',face:2},{iX:2,iY:1,iZ:2,axis:'z',face:2},{iX:2,iY:2,iZ:2,axis:'z',face:2},{iX:0,iY:0,iZ:0,axis:'x',face:3},{iX:0,iY:0,iZ:1,axis:'x',face:3},{iX:0,iY:0,iZ:2,axis:'x',face:3},{iX:0,iY:1,iZ:0,axis:'x',face:3},{iX:0,iY:1,iZ:1,axis:'x',face:3},{iX:0,iY:1,iZ:2,axis:'x',face:3},{iX:0,iY:2,iZ:0,axis:'x',face:3},{iX:0,iY:2,iZ:1,axis:'x',face:3},{iX:0,iY:2,iZ:2,axis:'x',face:3},{iX:2,iY:0,iZ:0,axis:'x',face:4},{iX:2,iY:0,iZ:1,axis:'x',face:4},{iX:2,iY:0,iZ:2,axis:'x',face:4},{iX:2,iY:1,iZ:0,axis:'x',face:4},{iX:2,iY:1,iZ:1,axis:'x',face:4},{iX:2,iY:1,iZ:2,axis:'x',face:4},{iX:2,iY:2,iZ:0,axis:'x',face:4},{iX:2,iY:2,iZ:1,axis:'x',face:4},{iX:2,iY:2,iZ:2,axis:'x',face:4},{iX:0,iY:0,iZ:0,axis:'y',face:5},{iX:0,iY:0,iZ:1,axis:'y',face:5},{iX:0,iY:0,iZ:2,axis:'y',face:5},{iX:1,iY:0,iZ:0,axis:'y',face:5},{iX:1,iY:0,iZ:1,axis:'y',face:5},{iX:1,iY:0,iZ:2,axis:'y',face:5},{iX:2,iY:0,iZ:0,axis:'y',face:5},{iX:2,iY:0,iZ:1,axis:'y',face:5},{iX:2,iY:0,iZ:2,axis:'y',face:5},{iX:0,iY:2,iZ:0,axis:'y',face:6},{iX:0,iY:2,iZ:1,axis:'y',face:6},{iX:0,iY:2,iZ:2,axis:'y',face:6},{iX:1,iY:2,iZ:0,axis:'y',face:6},{iX:1,iY:2,iZ:1,axis:'y',face:6},{iX:1,iY:2,iZ:2,axis:'y',face:6},{iX:2,iY:2,iZ:0,axis:'y',face:6},{iX:2,iY:2,iZ:1,axis:'y',face:6},{iX:2,iY:2,iZ:2,axis:'y',face:6}]", "as":"iX" }, { "type":"flatten", "fields":["iX"] }, { "type":"project", "fields":["iX.iX","iX.iY","iX.iZ","iX.axis","iX.face"], "as":["iX","iY","iZ","axis","face"] }, { "type":"formula", "expr":"datum.axis === 'x' ? {x:datum.iX===0?-1:1, y:0,z:0}: datum.axis === 'y' ? {x:0, y:datum.iY === 0 ? -1:1, z:0}: {x:0,y:0, z:datum.iZ ===0?-1:1}", "as":"normal" }, { "type":"formula", "expr":"datum.axis === 'x' ? {x:(datum.iX === cube_size - 1 ? cube_size : 0) - cube_size/2, y: (1/2 + datum.iY) - cube_size/2, z: (1/2 + datum.iZ) - cube_size/2}: datum.axis === 'y' ? {x:(1/2 + datum.iX)-cube_size/2, y: (datum.iY === cube_size - 1 ? cube_size:0) -cube_size/2, z:( 1/2 + datum.iZ)-cube_size/2} : {x:(1/2 + datum.iX)-cube_size/2, y: (1/2 + datum.iY)-cube_size/2, z: (datum.iZ === cube_size - 1 ? cube_size : 0)-cube_size/2}", "as":"center" }, { "type":"formula", "expr":"datum.axis === 'x' ? [{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2}] : datum.axis === 'y' ? 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If you don't do that, the cube positions are not updated and weird things begin to happen. **NOTE**: It's usefull at that point to have a reset button. The code is very simple. a signal is setting the points data to it's initial state which was an almost empty table (only one empty object). Doing that will make the points table to redo all the transforms, an recreate the points table (this is why the points data are in a formula). The points table being updated, it will recalculate the points_dynpoints_dyn table and the cube will be restored. ### Completing the uncompleted rotations As we don't want to force the user to do the perfect rotation, we want to complete the rotation so that when she releases the mouse, the rotation angle is always a multiple of 90. That kind of thing is quite tricky to achieve in Vega. This is because data changes propagation is done trough a graph. This is great to cascade the changes as we can see in these 3D experiments, but when you want to have a signal updating another without creating circle references it becomes a mind game. We won't complain about it because the goal of Vega is not to create games, but it's important to understand this. To be able to achieve the completion angle we have to: - Create a table unfinished with points_dyn as a source filtering the line that have a pending rotation - Create a variable last_Rotation that will react on mouse release and check if the unfinished table has any data. If there are data the variable will store the rotation information from the first object (all the object of the table have the same rotation at that point) - Create a variable completion_Angle that will listen to last_Rotation and create the completion_Angle accordingly - Modify the rotation_Line to listen to the completion_Angle Let's try this:`3d:T53de,embed({ "$schema": "https://vega.github.io/schema/vega/v5.json", "width":400, "height":400, "background":"black", "signals":[ { "name":"size", "init":"40*(min (width,height)/400)" }, { "name":"cube_padding", "value":0.02 }, { "name":"cube_size", "value":3 }, { "name":"btn_reset_pressed", "on":[{"events":"@btn_reset:mousedown,@txt_reset:mousedown", "update":"true"}, {"events":"@btn_reset:mouseup,@txt_reset:mouseup", "update":"false"}] }, { "name":"reset", "on": [{"events":"@btn_reset:mousedown,@txt_reset:mousedown", "update":"setdata('points',[{iX:[]}])"}, {"events":"@btn_reset:mouseup,@txt_reset:mouseup", "update":"0"}] }, { "name":"scale", "value":1, "bind":{"input":"range","min": 0, "max": 2, "step": 0.1}, "on":[{"events":"view:mousewheel", "update":"max(0, min(2, scale + (event.wheelDelta > 0 ? 0.1 : -0.1)))"}] }, { "name":"angle_HOR", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_HOR + (cube_changing ? 0 : ((event.movementX < 0) ^ (rotation_VER > 180) ? 5 : (event.movementX > 0) ^(rotation_VER > 180) ? -5 : 0))"}] }, { "name":"validAngle_HOR", "update":"angle_HOR % 360 <0 ? 360 + angle_HOR % 360 : angle_HOR % 360" }, { "name":"angle_VER", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "update":"rotation_VER + ( cube_changing ? 0 :(event.movementY < 0 ? 5 : event.movementY > 0 ? -5 : 0))"}] }, { "name":"angle_Line", "on":[{"events":{"source":"view", "type": "mousemove", "filter":"event.buttons === 1"}, "force": true,"update":"rotation_Line.angle === 0 && selected !=null ? ((selected.axis === 'z' ? (event.movementX < 0 ^ (rotation_VER > 180) ? 1 : event.movementX === 0 ? 0 : -1) : (selected.axis === 'x' ? (event.movementY < 0 ^ isYZBack ^ (rotation_VER > 180) ? 1 : event.movementY === 0 ? 0 : -1) : (selected.axis === 'y' ? (event.movementY < 0 ^ isXZBack ^ (rotation_VER > 180) ? 1 : event.movementY === 0 ? 0 : -1) : 0)))*10) : 0"}] }, { "name":"completion_Angle", "on":[{"events":{"signal":"last_Rotation"}, "update":"last_Rotation !== null && last_Rotation.rotation.a % 90 !== 0? {angle: last_Rotation.rotation.a % 90 === 0 ? 0 : abs(last_Rotation.rotation.a) % 90 < 40 ? -(last_Rotation.rotation.a % 90) : (last_Rotation.rotation.a < 0 ? -90 : 90) - last_Rotation.rotation.a % 90, axis: last_Rotation.rotation.r, iX:last_Rotation.iX, iY: last_Rotation.iY, iZ: last_Rotation.iZ}:{angle:0, axis:null, iX:-1, iY:-1, iZ:-1}"},{"events":"view:mousedown", "update":"selected !=null ? {angle:0, axis: selected.axis, iX: selected.iX, iY:selected.iY, iZ:selected.iZ}:{angle:0, axis:null, iX: -1, iY: -1, iZ: -1}"}] }, { "name":"last_Rotation", "on":[{"events":{"signal":"cube_changing"}, "update":"cube_changing? null : length(data('unfinished'))>0 ? data('unfinished')[0] : null"},{"events":{"signal":"reset"},"update":"null"}] }, { "name":"validAngle_VER", "update":"angle_VER % 360 <0 ? 360 + angle_VER % 360 : angle_VER % 360" }, { "name":"rotation_HOR", "value":45, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_HOR"}, "update":"validAngle_HOR"}] }, { "name":"rotation_VER", "value":65, "bind":{"input":"range", "min": 0, "max": 360, "step": 1}, "on":[{"events":{"signal":"validAngle_VER"}, "update":"validAngle_VER"}] }, { "name":"rotation_Line", "value":{"angle":0, "axis":null, "iX":-1, "iY":-1, "iZ":-1}, "on":[{"events":{"signal":"angle_Line"}, "update":"selected !== null ? {angle:angle_Line, axis : selected.axis, iX: selected.iX, iY:selected.iY, iZ:selected.iZ}: {angle:0, axis:null, iX:-1, iY:-1, iZ:-1}"},{"events":{"signal":"completion_Angle"}, "update":"completion_Angle"}] }, { "name":"qrAngle_HOR", "init":"PI*(rotation_HOR)/360", "on": [{"events":{"signal":"-rotation_HOR"}, "update":"PI*(rotation_HOR)/360"}] }, { "name":"qrAngle_VER", "init":"PI*(rotation_VER)/360", "on": [{"events":{"signal":"rotation_VER"}, "update":"PI*(rotation_VER)/360"}] }, { "name":"qrAngle_Line", "init":"PI*(rotation_Line.angle)/360", "on": [{"events":{"signal":"rotation_Line"}, "update":"PI*(rotation_Line.angle)/360"}] }, { "name":"qrw0", "update":"cos(qrAngle_VER)" }, { "name":"qrw1", "update":"cos(qrAngle_HOR)" }, { "name":"qrx0", "update":"sin(qrAngle_VER)" }, { "name":"qrz1", "update":"sin(qrAngle_HOR)" }, { "name":"q", "update":"{x:qrx0*qrw1, y:-qrx0*qrz1, z:qrw0*qrz1, w: qrw0*qrw1}" }, { "name":"q_1", "update":"{x:-q.x, y:-q.y, z: -q.z, w: q.w}" }, { "name":"qLine", "update":"{x: (rotation_Line.axis === 'y' ? sin(qrAngle_Line) : 0), y:(rotation_Line.axis === 'x' ? sin(-qrAngle_Line) : 0), z:(rotation_Line.axis === 'z' ? sin(qrAngle_Line) : 0), w : (rotation_Line.axis !==null ? cos(qrAngle_Line) : 1)}" }, { "name":"qLine_1", "update":"{x: -qLine.x, y: -qLine.y, z: -qLine.z, w: qLine.w}" }, { "name":"isYZBack", "update":"{z: 2*(q.x * q.z) - 2*(q.w * q.y)}.z < 0" }, { "name":"isXZBack", "update":"{z: 2*(q.y * q.z) + 2 *(q.w * q.x)}.z < 0" }, { "name":"isXYBack", "update":"{z: (q.z*q.z) - (q.y*q.y) - (q.x*q.x) + (q.w*q.w)}.z < 0" }, { "name":"perspective", "value":0.5, "bind":{"input":"range", "min": 0, "max": 2, "step": 0.05} }, { "name":"cube_changing", "init":"false", "on":[{"events":"view:mousedown", "update":"selected!=null"},{"events":"view:mouseup", "update":"false"}] }, { "name":"selected", "init":"null", "on":[ {"events":"@face:mousemove", "update":"event.buttons === 0 ?{iX:datum.iX, iY:datum.iY, iZ:datum.iZ, axis: (datum.iZ < cube_size - 1 && rotation_VER <= 180) || (datum.iZ !== 0 && rotation_VER > 180) ? 'z' : datum.axis} : selected"}, {"events":"@face:mouseout", "update":"cube_changing ? selected : null"}, {"events":"view:mouseup", "update":"null"} ] } ], "scales":[ { "name":"color", "type":"ordinal", "domain":[1,2,3,4,5,6], "range":["darkorange","red","yellow","white","green","blue"] } ], "data":[ { "name":"points", "values":[{"iX":[]}], "transform":[ { "type":"formula", "expr":"[{iX:0,iY:0,iZ:0,axis:'z',face:1},{iX:0,iY:1,iZ:0,axis:'z',face:1},{iX:0,iY:2,iZ:0,axis:'z',face:1},{iX:1,iY:0,iZ:0,axis:'z',face:1},{iX:1,iY:1,iZ:0,axis:'z',face:1},{iX:1,iY:2,iZ:0,axis:'z',face:1},{iX:2,iY:0,iZ:0,axis:'z',face:1},{iX:2,iY:1,iZ:0,axis:'z',face:1},{iX:2,iY:2,iZ:0,axis:'z',face:1},{iX:0,iY:0,iZ:2,axis:'z',face:2},{iX:0,iY:1,iZ:2,axis:'z',face:2},{iX:0,iY:2,iZ:2,axis:'z',face:2},{iX:1,iY:0,iZ:2,axis:'z',face:2},{iX:1,iY:1,iZ:2,axis:'z',face:2},{iX:1,iY:2,iZ:2,axis:'z',face:2},{iX:2,iY:0,iZ:2,axis:'z',face:2},{iX:2,iY:1,iZ:2,axis:'z',face:2},{iX:2,iY:2,iZ:2,axis:'z',face:2},{iX:0,iY:0,iZ:0,axis:'x',face:3},{iX:0,iY:0,iZ:1,axis:'x',face:3},{iX:0,iY:0,iZ:2,axis:'x',face:3},{iX:0,iY:1,iZ:0,axis:'x',face:3},{iX:0,iY:1,iZ:1,axis:'x',face:3},{iX:0,iY:1,iZ:2,axis:'x',face:3},{iX:0,iY:2,iZ:0,axis:'x',face:3},{iX:0,iY:2,iZ:1,axis:'x',face:3},{iX:0,iY:2,iZ:2,axis:'x',face:3},{iX:2,iY:0,iZ:0,axis:'x',face:4},{iX:2,iY:0,iZ:1,axis:'x',face:4},{iX:2,iY:0,iZ:2,axis:'x',face:4},{iX:2,iY:1,iZ:0,axis:'x',face:4},{iX:2,iY:1,iZ:1,axis:'x',face:4},{iX:2,iY:1,iZ:2,axis:'x',face:4},{iX:2,iY:2,iZ:0,axis:'x',face:4},{iX:2,iY:2,iZ:1,axis:'x',face:4},{iX:2,iY:2,iZ:2,axis:'x',face:4},{iX:0,iY:0,iZ:0,axis:'y',face:5},{iX:0,iY:0,iZ:1,axis:'y',face:5},{iX:0,iY:0,iZ:2,axis:'y',face:5},{iX:1,iY:0,iZ:0,axis:'y',face:5},{iX:1,iY:0,iZ:1,axis:'y',face:5},{iX:1,iY:0,iZ:2,axis:'y',face:5},{iX:2,iY:0,iZ:0,axis:'y',face:5},{iX:2,iY:0,iZ:1,axis:'y',face:5},{iX:2,iY:0,iZ:2,axis:'y',face:5},{iX:0,iY:2,iZ:0,axis:'y',face:6},{iX:0,iY:2,iZ:1,axis:'y',face:6},{iX:0,iY:2,iZ:2,axis:'y',face:6},{iX:1,iY:2,iZ:0,axis:'y',face:6},{iX:1,iY:2,iZ:1,axis:'y',face:6},{iX:1,iY:2,iZ:2,axis:'y',face:6},{iX:2,iY:2,iZ:0,axis:'y',face:6},{iX:2,iY:2,iZ:1,axis:'y',face:6},{iX:2,iY:2,iZ:2,axis:'y',face:6}]", "as":"iX" }, { "type":"flatten", "fields":["iX"] }, { "type":"project", "fields":["iX.iX","iX.iY","iX.iZ","iX.axis","iX.face"], "as":["iX","iY","iZ","axis","face"] }, { "type":"formula", "expr":"datum.axis === 'x' ? {x:datum.iX===0?-1:1, y:0,z:0}: datum.axis === 'y' ? {x:0, y:datum.iY === 0 ? -1:1, z:0}: {x:0,y:0, z:datum.iZ ===0?-1:1}", "as":"normal" }, { "type":"formula", "expr":"datum.axis === 'x' ? {x:(datum.iX === cube_size - 1 ? cube_size : 0) - cube_size/2, y: (1/2 + datum.iY) - cube_size/2, z: (1/2 + datum.iZ) - cube_size/2}: datum.axis === 'y' ? {x:(1/2 + datum.iX)-cube_size/2, y: (datum.iY === cube_size - 1 ? cube_size:0) -cube_size/2, z:( 1/2 + datum.iZ)-cube_size/2} : {x:(1/2 + datum.iX)-cube_size/2, y: (1/2 + datum.iY)-cube_size/2, z: (datum.iZ === cube_size - 1 ? cube_size : 0)-cube_size/2}", "as":"center" }, { "type":"formula", "expr":"datum.axis === 'x' ? [{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z - (1-cube_padding)/2}] : datum.axis === 'y' ? [{x:datum.center.x - (1-cube_padding)/2 , y:datum.center.y, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y, z : datum.center.z - (1-cube_padding)/2},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y, z : datum.center.z + (1-cube_padding)/2},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y, z : datum.center.z - (1-cube_padding)/2}] : [{x:datum.center.x - (1-cube_padding)/2 , y:datum.center.y - (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x + (1-cube_padding)/2, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y + (1-cube_padding)/2, z : datum.center.z},{x:datum.center.x - (1-cube_padding)/2, y:datum.center.y - (1-cube_padding)/2, z : datum.center.z}]", "as":"points" }, { "type":"formula", "expr":"{x:(datum.iX+1/2) - cube_size/2, y: (1/2 + datum.iY) - cube_size/2, z: (1/2 + datum.iZ) - cube_size/2}", "as":"center" }, { "type":"flatten", "fields":["points"] } ] }, { "name":"points_dyn", "source":"points", "transform":[ { "type":"formula", "expr":"(rotation_Line.angle !== 0 && rotation_Line.axis !== null && ((rotation_Line.axis === 'x' && datum.iY === rotation_Line.iY) || (rotation_Line.axis === 'y' && datum.iX === rotation_Line.iX) || (rotation_Line.axis === 'z' && datum.iZ === rotation_Line.iZ)))", "as":"isTransformed" }, { "type":"formula", "expr":"datum.isTransformed?{x:qLine.w * datum.normal.x + qLine.y*datum.normal.z- qLine.z * datum.normal.y, y:qLine.w * datum.normal.y - qLine.x * datum.normal.z + qLine.z*datum.normal.x, z:qLine.w * datum.normal.z + qLine.x*datum.normal.y - qLine.y * datum.normal.x, w: -qLine.x * datum.normal.x - qLine.y * datum.normal.y - qLine.z * datum.normal.z}:{}", "as":"q1" }, { "type":"formula", "expr":"datum.isTransformed?{x:datum.q1.w * qLine_1.x + datum.q1.x * qLine_1.w + datum.q1.y * qLine_1.z - datum.q1.z * qLine_1.y, y:datum.q1.w * qLine_1.y - datum.q1.x * qLine_1.z + datum.q1.y * qLine_1.w + datum.q1.z * qLine_1.x,z:datum.q1.w * qLine_1.z + datum.q1.x * qLine_1.y - datum.q1.y * qLine_1.x + datum.q1.z * qLine_1.w}:datum.normal", "as":"normal" }, { "type":"formula", "expr":"datum.isTransformed?{x:qLine.w * datum.center.x + qLine.y*datum.center.z- qLine.z * datum.center.y, y:qLine.w * datum.center.y - qLine.x * datum.center.z + qLine.z*datum.center.x, z:qLine.w * datum.center.z + qLine.x*datum.center.y - qLine.y * datum.center.x, w: -qLine.x * datum.center.x - qLine.y * datum.center.y - qLine.z * datum.center.z}: {}", "as":"q1" }, { "type":"formula", "expr":"datum.isTransformed?{x:datum.q1.w * qLine_1.x + datum.q1.x * qLine_1.w + datum.q1.y * qLine_1.z - datum.q1.z * qLine_1.y, y:datum.q1.w * qLine_1.y - datum.q1.x * qLine_1.z + datum.q1.y * qLine_1.w + datum.q1.z * qLine_1.x,z:datum.q1.w * qLine_1.z + datum.q1.x * qLine_1.y - datum.q1.y * qLine_1.x + datum.q1.z * qLine_1.w}: datum.center", "as":"center" }, { "type":"formula", "expr":"datum.isTransformed?{x:qLine.w * datum.points.x + qLine.y*datum.points.z- qLine.z * datum.points.y, y:qLine.w * datum.points.y - qLine.x * datum.points.z + qLine.z*datum.points.x, z:qLine.w * datum.points.z + qLine.x*datum.points.y - qLine.y * datum.points.x, w: -qLine.x * datum.points.x - qLine.y * datum.points.y - qLine.z * datum.points.z}:{}", "as":"q1" }, { "type":"formula", "expr":"datum.isTransformed?{x:datum.q1.w * qLine_1.x + datum.q1.x * qLine_1.w + datum.q1.y * qLine_1.z - datum.q1.z * qLine_1.y, y:datum.q1.w * qLine_1.y - datum.q1.x * qLine_1.z + datum.q1.y * qLine_1.w + datum.q1.z * qLine_1.x,z:datum.q1.w * qLine_1.z + datum.q1.x * qLine_1.y - datum.q1.y * qLine_1.x + datum.q1.z * qLine_1.w}:datum.points", "as":"points" }, { "type":"formula", "expr":"datum.isTransformed ? {r:rotation_Line.axis, a: ((isDefined(datum.rotation) ? datum.rotation.a: 0) + rotation_Line.angle)} : datum.rotation", "as":"rotation" }, { "type":"formula", "expr":"!cube_changing && isValid(datum.rotation) && datum.rotation.a!==0", "as":"isUpdated" }, { "type":"formula", "expr":"datum.isUpdated && datum.rotation.a % 90 === 0 ? 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The main problem is that the index is changing while the data are still processing and it creates a lot of trouble. I solved this sending 5 degreed then 0 rotations and wait that the unfinished table to be empty to switch the index. Then I had still one issue. Rotations of 180 were not taken in account. I used a counter based on rotation angle divided by 90 to ensure not to change the index while the counter was not reached. It seems a little complicate, but I didn't found other solution to make it work... ## Known issues - The stroke lines are not perfect - There are some clipping issues when the perspective factor is increasing - There are some clipping issues when rotating a line - Sometimes the history won't get the event, and the solving system fails miserabily ## Conslusion This was clearly my most complicated challenge in Vega and I'm really to not have given up trying to find solutions. During the process, I was asking to my self and you probably had the same thoughts reading this: > Why I'm doing this? Well, I think the most honnest answer is: I can't help myself. Another answer is that I love the spirit of Vega, so I love to challenge it. I also think that we really learn something trying to achieve crazy things...`41:[] 2e:{"title":"The Rubik's Cube","cells":[{"id":0,"value":"title = md`# The Rubik's Cube#\nThe Rubik's Cube - one of the world's best selling toys - is a 3-D puzzle that was invented by Hungarian professor of architecture Ernő Rubik in 1974.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"help = md`*Drag the view outside the cube to rotate it and, drag into the cube to rotate a face. You can also use the mouse wheel to change the scale of the cube.
\nHit 'Calculate' button to see how many possible arrangements a rubik's cube can be shuffled.*`","pinned":false,"hidden":false,"mode":"ojs"},{"id":234,"value":"viewof button = html`
${Object.assign(html`