31:T6a6,# Jump Flood Algorithm for Buffering Raster Images This notebook illustrates drawing a filled buffer region around drawn raster images. It uses rasterized lines as input, but the input geometry could be lines, polygons, single pixels; any raster input, really. The naive approach iterates over a local neighborhood and computes the distance to the nearest filled pixel. However, for a ${tex`n \times n`} image and a radius-${tex`m`} neighborhood, this has ${tex`O(n^2 m^2)`} complexity, which approaches ${tex`O(n^4)`} as the radius becomes large. That's completely impractical! Instead, this notebook performs this buffering using the [Jump Flood Algorithm](https://observablehq.com/@mourner/discrete-voronoi-with-jump-flooding), which performs roughly ${tex`\lceil\log_2(N)\rceil`} steps, where N is ${tex`\max(\mathrm{width},\mathrm{height})`}. Its secret sauce is transmitting the location of the nearest pixel distances much larger than a single pixel on early iterations, and then refining the details on later iterations. The result is that in a fixed number of steps, we can efficiently draw a buffered region. One additional optimization is that I've truncated the initial step size of the algorithm since we don't need to start at the full image size. Instead, we can start at the next nearest power of two since the buffer radius defines the maximum distance information can travel anyway. On a somewhat unrelated note, I've also add a blur pass using stackblur since I'll need it for my particular application. I've pared it down to a single channel, but even for RGBA images, stackblur is exceptionally fast! Click and draw below to draw curves and observe the buffer drawn around it.32:Taeb,viewof input = { const [w, h] = shape; const outerContainer = document.createElement("div"); const container = document.createElement("div"); container.style.cssText = ` image-rendering: pixelated; position: relative; width: ${shape[0]}px; height: ${shape[1]}px; border:1px solid #ccc; cursor:pointer;`; const canvas = DOM.canvas(...shape); canvas.style.cssText = "position:absolute;top:0;left:0"; const ctx = canvas.getContext("2d", { willReadFrequently: true }); const resultCanvas = DOM.canvas(...shape); resultCanvas.style.cssText = "position:absolute;top:0;left:0;pointer-events:none;opacity:0.5"; const resultCtx = resultCanvas.getContext("2d", { willReadFrequently: true }); const clearBtn = htl.html``; clearBtn.addEventListener("click", clear); container.appendChild(canvas); container.appendChild(resultCanvas); outerContainer.append(container); outerContainer.append(clearBtn); const pixels = new Uint8Array(canvas.width * canvas.height); outerContainer.value = { ctx, pixels, resultCtx }; clear(); ctx.beginPath(); ctx.lineWidth = 2; ctx.moveTo(w * 0.2, h * 0.25); ctx.lineTo(w * 0.4, h * 0.75); ctx.lineTo(w * 0.6, h * 0.25); ctx.lineTo(w * 0.8, h * 0.75); ctx.stroke(); emitUpdate(); let prevX = NaN; let prevY = NaN; function onMousedown(event) { prevX = NaN; prevY = NaN; canvas.addEventListener("mousemove", onMousemove); window.addEventListener("mouseup", onMouseup); drawPixel(event, ~opts.indexOf("Live update")); } function onMousemove(event) { drawPixel(event, ~opts.indexOf("Live update")); } function onMouseup(event) { canvas.removeEventListener("mousemove", onMousemove); window.removeEventListener("mouseup", onMouseup); drawPixel(event); } function drawPixel({ clientX, clientY }, emit = true) { const rect = canvas.getBoundingClientRect(); const x = Math.floor(clientX - rect.left); const y = Math.floor(clientY - rect.top); if (!isNaN(prevX)) { ctx.lineWidth = 2; ctx.strokeStyle = "black"; ctx.beginPath(); ctx.moveTo(prevX, prevY); ctx.lineTo(x, y); ctx.stroke(); } if (emit) emitUpdate(); prevX = x; prevY = y; } function clear() { ctx.fillStyle = "rgba(255,255,255,1)"; ctx.fillRect(0, 0, w, h); resultCtx.fillStyle = "rgba(0,0,0,0)"; resultCtx.fillRect(0, 0, w, h); emitUpdate(); } function emitUpdate() { outerContainer.dispatchEvent(new CustomEvent("input")); const input = ctx.getImageData(0, 0, w, h).data; for (let i = 0, n = w * h; i < n; i++) { pixels[i] = 255 - input[i * 4]; } } canvas.addEventListener("mousedown", onMousedown); return outerContainer; }33:T999,function jumpFloodBuffer(pixels, w, h, radius = 0, feather = 0) { const t0 = performance.now(); const n = w * h; const pixelsIn = pixels.slice(); // initialize a grid that keeps track of the closest data point for each pixel const EMPTY = new Uint32Array([-1])[0]; const closest = new Uint32Array(w * h); // init data points as closest to themselves for (let i = 0; i < n; i++) { closest[i] = pixels[i] > 128 ? i : EMPTY; } // starting flood step is the half of the grid size's closest power of two const maxRadius = radius + feather * 0.5; const maxStep = 2 ** Math.ceil(Math.log2(Math.min(maxRadius / 2, Math.max(w, h)))); //if (false) pass(1); // an optional 1-step pass that increases precision // run passes at e.g. 512, 256, 128, ..., 1 for (let step = maxStep; step >= 1; step >>= 1) { for (let y = 0; y < h; y++) { for (let x = 0; x < w; x++) { const k = x + w * y; let bestSeed = EMPTY; for (let i = -step, bestDist = Infinity; i <= step; i += step) { const y0 = y + i; if (y0 < 0 || y0 >= h) continue; for (let j = -step; j <= step; j += step) { const x0 = x + j; if (x0 < 0 || x0 >= w) continue; const m = x0 + w * y0; if (pixels[m] === 0) continue; const seed = closest[m]; const dx = x - (seed % w); const dy = y - ((seed / w) | 0); const d = dx * dx + dy * dy; if (d < bestDist) { bestDist = d; bestSeed = seed; } } } if (bestSeed === EMPTY) continue; closest[k] = bestSeed; pixels[k] = pixels[bestSeed]; } } } // Turn our computation of the closest raster pixel index into a floating point distance const f = Math.max(feather, 1e-8); const a = radius - f * 0.5; const b = radius + f * 0.5; for (let y0 = 0; y0 < h; y0++) { for (let x0 = 0; x0 < w; x0++) { const idx = x0 + w * y0; const closestIdx = closest[idx]; if (closestIdx === EMPTY) { pixels[idx] = 0; continue; } const dx = x0 - (closestIdx % w); const dy = y0 - ((closestIdx / w) | 0); const dist = Math.sqrt(dx * dx + dy * dy); pixels[idx] = 255 * linearstep(b, a, dist); } } const t1 = performance.now(); mutable jumpFloodMs = Math.round(10 * (t1 - t0)) * 0.1; return pixels; }34:T1b49,stackblur = { /* StackBlur - a fast almost Gaussian Blur For Canvas Version: 0.5 Author: Mario Klingemann Contact: mario@quasimondo.com Website: http://www.quasimondo.com/StackBlurForCanvas Twitter: @quasimondo In case you find this class useful - especially in commercial projects - I am not totally unhappy for a small donation to my PayPal account mario@quasimondo.de Or support me on flattr: https://flattr.com/thing/72791/StackBlur-a-fast-almost-Gaussian-Blur-Effect-for-CanvasJavascript Copyright (c) 2010 Mario Klingemann Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ // prettier-ignore var mul_table = [ 512,512,456,512,328,456,335,512,405,328,271,456,388,335,292,512, 454,405,364,328,298,271,496,456,420,388,360,335,312,292,273,512, 482,454,428,405,383,364,345,328,312,298,284,271,259,496,475,456, 437,420,404,388,374,360,347,335,323,312,302,292,282,273,265,512, 497,482,468,454,441,428,417,405,394,383,373,364,354,345,337,328, 320,312,305,298,291,284,278,271,265,259,507,496,485,475,465,456, 446,437,428,420,412,404,396,388,381,374,367,360,354,347,341,335, 329,323,318,312,307,302,297,292,287,282,278,273,269,265,261,512, 505,497,489,482,475,468,461,454,447,441,435,428,422,417,411,405, 399,394,389,383,378,373,368,364,359,354,350,345,341,337,332,328, 324,320,316,312,309,305,301,298,294,291,287,284,281,278,274,271, 268,265,262,259,257,507,501,496,491,485,480,475,470,465,460,456, 451,446,442,437,433,428,424,420,416,412,408,404,400,396,392,388, 385,381,377,374,370,367,363,360,357,354,350,347,344,341,338,335, 332,329,326,323,320,318,315,312,310,307,304,302,299,297,294,292, 289,287,285,282,280,278,275,273,271,269,267,265,263,261,259]; // prettier-ignore var shg_table = [ 9, 11, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24 ]; return function blurSingle(pixels, width, height, radius) { const t0 = performance.now(); if (isNaN(radius) || radius < 1) return pixels; radius |= 0; var x, y, i, p, yp, yi, yw, r_sum, r_out_sum, r_in_sum, pr, rbs; var div = radius + radius + 1; var widthMinus1 = width - 1; var heightMinus1 = height - 1; var radiusPlus1 = radius + 1; var sumFactor = (radiusPlus1 * (radiusPlus1 + 1)) / 2; var stackStart = new BlurStack(); var stack = stackStart; for (i = 1; i < div; i++) { stack = stack.next = new BlurStack(); if (i == radiusPlus1) var stackEnd = stack; } stack.next = stackStart; var stackIn = null; var stackOut = null; yw = yi = 0; var mul_sum = mul_table[radius]; var shg_sum = shg_table[radius]; for (y = 0; y < height; y++) { r_in_sum = r_sum = 0; r_out_sum = radiusPlus1 * (pr = pixels[yi]); r_sum += sumFactor * pr; stack = stackStart; for (i = 0; i < radiusPlus1; i++) { stack.r = pr; stack = stack.next; } for (i = 1; i < radiusPlus1; i++) { p = yi + (widthMinus1 < i ? widthMinus1 : i) /* << 2 */; r_sum += (stack.r = pr = pixels[p]) * (rbs = radiusPlus1 - i); r_in_sum += pr; stack = stack.next; } stackIn = stackStart; stackOut = stackEnd; for (x = 0; x < width; x++) { pixels[yi] = (r_sum * mul_sum) >> shg_sum; r_sum -= r_out_sum; r_out_sum -= stackIn.r; p = yw + ((p = x + radius + 1) < widthMinus1 ? p : widthMinus1); // << 2; r_in_sum += stackIn.r = pixels[p]; r_sum += r_in_sum; stackIn = stackIn.next; r_out_sum += pr = stackOut.r; r_in_sum -= pr; stackOut = stackOut.next; yi++; } yw += width; } for (x = 0; x < width; x++) { r_in_sum = r_sum = 0; yi = x; // << 2; r_out_sum = radiusPlus1 * (pr = pixels[yi]); r_sum += sumFactor * pr; stack = stackStart; for (i = 0; i < radiusPlus1; i++) { stack.r = pr; stack = stack.next; } yp = width; for (i = 1; i <= radius; i++) { yi = yp + x; r_sum += (stack.r = pr = pixels[yi]) * (rbs = radiusPlus1 - i); r_in_sum += pr; stack = stack.next; if (i < heightMinus1) { yp += width; } } yi = x; stackIn = stackStart; stackOut = stackEnd; for (y = 0; y < height; y++) { p = yi; pixels[p] = (r_sum * mul_sum) >> shg_sum; r_sum -= r_out_sum; r_out_sum -= stackIn.r; p = x + ((p = y + radiusPlus1) < heightMinus1 ? p : heightMinus1) * width; r_sum += r_in_sum += stackIn.r = pixels[p]; stackIn = stackIn.next; r_out_sum += pr = stackOut.r; r_in_sum -= pr; stackOut = stackOut.next; yi += width; } } const t1 = performance.now(); mutable stackblurMs = Math.round(10 * (t1 - t0)) * 0.1; return pixels; }; function BlurStack() { this.r = 0; this.next = null; } }35:[] 2f:{"title":"Jump Flood Algorithm for Buffering Raster Images","cells":[{"id":315,"value":"$31","pinned":false,"hidden":false,"mode":"md"},{"id":298,"value":"viewof opts = Inputs.checkbox([\"Live update\"], {\n value: []\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":149,"value":"viewof radius = Inputs.range([0, 100 + 0 * Math.hypot(...shape)], {\n label: \"Buffer radius\",\n value: 20,\n step: 0.1 \n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":415,"value":"viewof feather = Inputs.range([0, 80], {\n label: \"Feather radius\",\n value: 1,\n step: 0.1\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":566,"value":"viewof blurRadius = Inputs.range([0, 100], {\n label: \"Blur radius\",\n value: 1\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":5,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":825,"value":"mutable jumpFloodMs = null","pinned":false,"hidden":false,"mode":"ojs"},{"id":830,"value":"mutable stackblurMs = null","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"shape = [2 ** Math.floor(Math.log2(width)), 2 ** Math.floor(Math.log2(width))]","pinned":false,"hidden":false,"mode":"ojs"},{"id":88,"value":"buffered = jumpFloodBuffer(input.pixels.slice(), ...shape, radius, feather)","pinned":true,"hidden":false,"mode":"ojs"},{"id":271,"value":"blurred = stackblur(buffered.slice(), ...shape, blurRadius)","pinned":true,"hidden":false,"mode":"ojs"},{"id":141,"value":"drawResult = {\n const imageData = input.resultCtx.getImageData(0, 0, ...shape);\n imageData.data.set(toImage(blurred, ...shape));\n input.resultCtx.putImageData(imageData, 0, 0);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":642,"value":"## Functions","pinned":false,"hidden":false,"mode":"md"},{"id":750,"value":"$33","pinned":true,"hidden":false,"mode":"ojs"},{"id":669,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":622,"value":"function toImage(array, width, height) {\n const output = new Uint8ClampedArray(width * height * 4);\n for (let y = 0; y < height; y++) {\n for (let x = 0; x < width; x++) {\n const idx = x + y * width;\n output[4 * idx] = 255;\n output[4 * idx + 1] = 0;\n output[4 * idx + 2] = 0;\n output[4 * idx + 3] = array[idx];\n }\n }\n return output;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":736,"value":"function smoothstep(min, max, value) {\n var x = Math.max(0, Math.min(1, (value - min) / (max - min)));\n return x * x * (3 - 2 * x);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":956,"value":"function linearstep(min, max, value) {\n return Math.max(0, Math.min(1, (value - min) / (max - min)));\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W35","stdlib":"1","titling":"auto"}