2f:T627,## Parametric generation of an ellipse's signed distance function The implicit formula of an ellipse is: ${tex`\frac{x^2}{a^2} + \frac{y^2}{b^2} = C^2`} With implicit, I mean that this function describes all ellipses with a radius of C. If we want to obtain the signed distance function (sdf) for an ellipse with an specific **size** then we substract the target size C from the function. Then, we can obtain the contour by running marching squares with an isovalue of 0. We use the **ellipticity** to define the relationship between the ${tex`a \text{ and } b`} parameters. The formula for ellipticity ${tex`e`} is: ${tex`e = \sqrt{\frac{a^2 - b^2}{a^2}}`} if ${tex`b < a`}, and ${tex`e = \sqrt{\frac{b^2 - a^2}{b^2}}`} if ${tex`a < b`} The maximum value that ${tex`a \text{ and } b`} can have is 1. Otherwise they will not fit in the defined ${tex`[-1,1]^2`} square. If ${tex`a=1 \text{ and } b=1`} then we have ${tex`e=0`} If ${tex`a=1 \text{ and } b=0.9`} then we have ${tex`e=0.43`} If ${tex`a=1 \text{ and } b=0.5`} then we have ${tex`e=0.86`} If ${tex`a=1 \text{ and } b=0.1`} then we have ${tex`e=0.99`} This shows that ${tex`e`} has an asymptote at 1. We will fix ${tex`a`} to 1 and will allow the user to vary the ellipticity from 0 (perfect circle) to 1 (oblate spheroid). As for the **rotation**, we allow rotating the XY plane by ${tex`\theta`} degrees. Finally, we allow contaminating the ellipse's contour with **${tex`\theta`}-correlated noise**. We expose several parameters of the noise function for you to explore its effect on the final contour.30:T88e,function generate_ellipse_sdf(w, h, ellipticity, isovalue, rotation_deg, noise_params={}){ // Initialize variables let a = 1; // we only allow oblate spheroid. Possible to obtain prolate one with rotation. let b = -((ellipticity ** 2) * (a ** 2) - (a ** 2)); // define b in relation to a based on ellipticity let rd = rotation_deg * (Math.PI/180.0); // from deg to rad if(!("freq1" in noise_params)) noise_params.freq1 = 1.0; if(!("freq2" in noise_params)) noise_params.freq2 = 1.0; if(!("amplitude1" in noise_params)) noise_params.amplitude1 = 1.0; if(!("amplitude2" in noise_params)) noise_params.amplitude2 = 1.0; if(!("weight" in noise_params)) noise_params.weight = 0.0; let [x, y, x1, y1, theta] = [0, 0, 0, 0, 0]; let [dist, signed_dist] = [0, 0]; let noise = 0; let noisy_dist = 0; // Generative loop let matrix = []; for(let r=0; r d3.min(d)));\n const max = d3.max(ellipse.map(d => d3.max(d)));\n const color_scale = d3.scaleDiverging([min, 0, max], d3.interpolatePuOr);\n\n for(let r=0; r d === 0? 1 : d), {value: 10, label: \"Num members\"});","pinned":false,"hidden":false,"mode":"ojs"},{"id":275,"value":"ensemble_params = get_ensemble_params(num_members, d3.randomNormal(0.6, 0.1), d3.randomNormal(0.7, 0.1), d3.randomNormal(45, 5))","pinned":false,"hidden":false,"mode":"ojs"},{"id":282,"value":"ensemble = get_ensemble_ellipses_sdfs(w, h, ensemble_params)","pinned":false,"hidden":false,"mode":"ojs"},{"id":258,"value":"viewof member_id = Inputs.range([0, num_members - 1], {value: 0, step: 1, label: \"Member id\"});","pinned":false,"hidden":false,"mode":"ojs"},{"id":303,"value":"{\n let ellipse = ensemble[member_id];\n \n let nrows = ellipse.length;\n let ncols = ellipse[0].length;\n\n const canvas = DOM.canvas(w, h);\n const ctx = canvas.getContext(\"2d\");\n\n ensemble.forEach(member => {\n plot_isocurve(ctx, member, 0, {color: color_secondary, opacity: 0.1});\n });\n plot_isocurve(ctx, ensemble[member_id], 0, {color: color_accent});\n\n return canvas;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":247,"value":"{\n let ellipse = ensemble[member_id];\n \n let nrows = ellipse.length;\n let ncols = ellipse[0].length;\n\n const canvas = DOM.canvas(w, h);\n const ctx = canvas.getContext(\"2d\");\n const min = d3.min(ellipse.map(d => d3.min(d)));\n const max = d3.max(ellipse.map(d => d3.max(d)));\n const color_scale = d3.scaleDiverging([min, 0, max], d3.interpolatePuOr);\n\n for(let r=0; r {\n return generate_ellipse_sdf(w, h, mp.ellipticity, mp.size, mp.rotation_deg);\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":394,"value":"## Imports","pinned":false,"hidden":false,"mode":"md"},{"id":18,"value":"d3 = import(\"d3\")","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}