How to smoothly align rotated bitmaps side by side without jerkiness?-CodePudding

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Is there a way to remove the grid jerkiness without doing it as a single pass and keeping the same interpolation scheme ?

Is it a sub pixels correctness issue ?

Here is some code :

let tileImage = null function preload() { tileImage = loadImage('data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAABACAYAAACqaXHeAAAMeHpUWHRSYXcgcHJvZmlsZSB0eXBlIGV4aWYAAHjarZhpktw6DoT/8xRzBO7LcbhGzA3m PMBlKq77eeIN0tXuKSiKBIEkImEzf7XP4/5B38hhmhiKjW3nC1/scXmOzfV3r h385G/da/ Dzi949x83ngGQpcw/3Z/DO GefePb/bs4l7578LvTeuc5e HvT jI f4 NZ0NdfF3osCO7ubNfzwrNQ8I9Fj nzsSi3Wn4cbc1n5/gM1a9/MRSfU3Yl8h29LSU37qu3seDPJYaGottb8 70Dry/36kem/wOLli Q3isDPLPh864fNtQjUxkQpcQ8p2CU8dbQokJLNzuwqfbjzO/ bLR3/4 zvHsmxy9s0J8 vKv bN5879YfxJg0/Uan4ehJ9htflz/ctxl96F3gfhs4//vnOdn51/jK/y5L19ffQt3OesevTQnKLHjC/yc6j3KHrHvCFe1Lcyn2KzIWsrN/JpfKrtdpICy052HNw354n9cdEt191xW6/TTUyMfvvC1ftpfNDBSpCan2SE00SI7vgSWlihkh5TcygG/7HF6bZNt5uu2mXsckz1jsWcJtl/ TF/d I5giXnbP34Cru8oAErrCP8cmEaEXHncWpSB7 fX/8kroEIJnVz5YDdDnOXGMl9JVfQQAcmJq4Xe66sZwFcxNYJY1wgAja7kFzGouJ9cQ5HVgLUMd2H6AcRcCn5hZE hpAJDuhgb94pTqf65O8wrArVAtMcCrFpoROsGBP5U2Ilh3oKKaaUciqpppZ6DlmQl3PJQs 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for (let x = 0; x < currentTileWidth; x = 1) { let ui = u let vi = v if (ui >= 0 && ui < tileImage.width) { let index1 = (floor(ui) floor(vi) * tileImage.width) * 4 let index2 = (x ox (y oy) * width) * 4 pixels[index2 0] = tileImage.pixels[index1 0] pixels[index2 1] = tileImage.pixels[index1 1] pixels[index2 2] = tileImage.pixels[index1 2] } u = dru v = drv } ru = dcu rv = dcv } } let angle = 0 function draw() { background(0) const s = sin(angle / 256 * PI * 2) const c = cos(angle / 256 * PI * 2) // compute rotated tile width / height let tw = tileImage.width let th = tileImage.height if (angle % 128 < 64) { currentTileWidth = abs(tw * c th * s) currentTileHeight = abs(tw * s th * c) } else { currentTileWidth = abs(tw * c - th * s) currentTileHeight = abs(tw * s - th * c) } currentTileWidth_d2 = (currentTileWidth / 2.0) currentTileHeight_d2 = (currentTileHeight / 2.0) // compute rotated point const rp = computeRotatedPoint(c, s, tw, 0) // draw tiles loadPixels() for (let i = -3; i <= 3; i = 1) { // compute center const cx = width / 2 - currentTileWidth_d2 const cy = height / 2 - currentTileHeight_d2 // compute tile position const ox = rp.x * i const oy = rp.y * i drawRotatedBitmap(c, s, round(cx ox), round(cy oy)) } updatePixels() angle = 0.5 }

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CodePudding user response：

Is there a way to remove the grid jerkiness without doing it as a single pass and keeping the same interpolation scheme ?

No

Is it a sub pixels correctness issue ?

No, it is an interpolation issue

CodePudding user response：

The frameCount is a function of the frameRate (which is not a constant contrary to what we think even if we set it), the execution time of the cycling draw function and the runtime environment (canvas or the gif one). It seems that for the gif the frameCount is reset to zero after a certain cumulated count, which corresponds to a reset to the vertical position of the image.
I tried to reproduce the "jerking effect" by changing the 64 parameter in the following instruction and the frameRate, without success.

if (frameCount % 128 < 64) {

I suggest to make the rotation speed independent of the frameCount.

CodePudding user response：

I have found a solution which does not use the same algorithm but use the same interpolation scheme.

Solution with a three-shear method

This solution use a three-pass shear method and the solution to fix the tiles jerkiness is to add the tile offset before the rotation and then round coordinates once everything is ready to be drawn :

/** * Bitmap rotation stable tiling with 3-shearing method * The 3-shearing method is stable between -PI / 2 and PI / 2 only, that is why a flip is needed for a full rotation * * https://www.ocf.berkeley.edu/~fricke/projects/israel/paeth/rotation_by_shearing.html */ let tex = null let tile = [] function preload() { tile = loadImage('data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAABACAYAAACqaXHeAAAMeHpUWHRSYXcgcHJvZmlsZSB0eXBlIGV4aWYAAHjarZhpktw6DoT/8xRzBO7LcbhGzA3m PMBlKq77eeIN0tXuKSiKBIEkImEzf7XP4/5B38hhmhiKjW3nC1/scXmOzfV3r h385G/da/ Dzi949x83ngGQpcw/3Z/DO GefePb/bs4l7578LvTeuc5e HvT jI f4 NZ0NdfF3osCO7ubNfzwrNQ8I9Fj nzsSi3Wn4cbc1n5/gM1a9/MRSfU3Yl8h29LSU37qu3seDPJYaGottb8 70Dry/36kem/wOLli Q3isDPLPh864fNtQjUxkQpcQ8p2CU8dbQokJLNzuwqfbjzO/ bLR3/4 zvHsmxy9s0J8 vKv bN5879YfxJg0/Uan4ehJ9htflz/ctxl96F3gfhs4//vnOdn51/jK/y5L19ffQt3OesevTQnKLHjC/yc6j3KHrHvCFe1Lcyn2KzIWsrN/JpfKrtdpICy052HNw354n9cdEt191xW6/TTUyMfvvC1ftpfNDBSpCan2SE00SI7vgSWlihkh5TcygG/7HF6bZNt5uu2mXsckz1jsWcJtl/ TF/d 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ox, oy, cx, cy) { for (let ty = 0; ty < tile.height; ty = 1) { for (let tx = 0; tx < tile.width; tx = 1) { // center of rotation let scx = tile.width - tx - tile.width / 2 let scy = tile.height - ty - tile.height / 2 // this is key to a stable rotation without any jerkiness scx = cx scy = cy // shear let ux = round(_shearX(t, scx, scy)) let uy = round(_shearY(s, ux, scy)) ux = round(_shearX(t, ux, uy)) // translate again ux = currentTileWidth_d2 - ux uy = currentTileHeight_d2 - uy // plot with offset let index1 = currentTileLookupFunction(tx, ty) let index2 = (ox ux (oy uy) * width) * 4 pixels[index2 0] = tile.pixels[index1 0] pixels[index2 1] = tile.pixels[index1 1] pixels[index2 2] = tile.pixels[index1 2] } } } let angle = -3.141592653 / 2 function draw() { const s = sin(angle) const c = cos(angle) const t = tan(angle / 2) tile.loadPixels() background(0) // compute rotated tile width / height let tw = tile.width let th = tile.height currentTileWidth = abs(tw * c th * s) currentTileHeight = abs(tw * s th * c) currentTileWidth_d2 = round(currentTileWidth / 2.0) currentTileHeight_d2 = round(currentTileHeight / 2.0) // draw tiles loadPixels() for (let j = -2; j <= 2; j = 1) { for (let i = -2; i <= 2; i = 1) { let ox = round(width / 2 - currentTileWidth_d2) let oy = round(height / 2 - currentTileHeight_d2) drawRotatedBitmap(c, s, t, ox, oy, i * tw, j * tw) } } updatePixels() angle = 0.025 if (angle >= PI / 2) { angle -= PI if (currentTileLookupFunction === tileLookup2) { currentTileLookupFunction = tileLookup1 } else { currentTileLookupFunction = tileLookup2 } } }

<!DOCTYPE html> <html lang="en"> <head> <script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.5.0/p5.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.5.0/addons/p5.sound.min.js"></script> <link rel="stylesheet" type="text/css" href="style.css"> <meta charset="utf-8" /> </head> <body> <main> </main> </body> </html>

I cannot say technically why it works but it is probably related to the interpolation since i can reproduce the question issue completely with the three-shear method if i add the tile offset after rotation and round the offset and shear pass independently such as :

function drawRotatedBitmap(c, s, t, ox, oy, cx, cy) { cx = round(_shearX(t, cx, cy)) cy = round(_shearY(s, cx, cy)) cx = round(_shearX(t, cx, cy)) for (let ty = 0; ty < tex.height; ty = 1) { ... let ux = round(_shearX(t, scx, scy)) let uy = round(_shearY(s, ux, scy)) ux = round(_shearX(t, ux, uy)) ... let index2 = (cx ux ox (cy uy oy) * width) * 4 ... } }

The interpolation issue become clearly visible if i round the offset and the shearing result at the same time which result in missing pixels in the final image such as :

function drawRotatedBitmap(c, s, t, ox, oy, cx, cy) { cx = _shearX(t, cx, cy) cy = _shearY(s, cx, cy) cx = _shearX(t, cx, cy) for (let ty = 0; ty < tex.height; ty = 1) { ... let ux = _shearX(t, scx, scy) let uy = _shearY(s, ux, scy) ux = _shearX(t, ux, uy) ... let index2 = (round(cx ux) ox (round(cy uy) oy) * width) * 4 ... } }

I would still like a detailed explanation of the jerkiness behavior and to know if there is a smooth solution by adding the tile offset after the rotation.