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    <p>I think you will never get an accurate result... I spent some time investigating how to do 3d graphics using canvas 2d context and I found it viable to do texture mapping gouraud shading by computing appropriate 2d gradients and matrices:</p> <ul> <li>Solid polygons are of course easy</li> <li>Gouraud filling is possible only on one component (i.e. you cannot have a triangle where every vertex is an arbitrary RGB filled with bilinear interpolation, but you can do that filling using for example three arbitrary shades of a single color)</li> <li>Linear texture mapping can be done using clipping and image drawing</li> </ul> <p>I would implement perspective-correct texture mapping using mesh subdivision (like on PS1).</p> <p>However I found many problems... for example image drawing with a matrix transform (needed for texture mapping) is quite inaccurate on chrome and IMO it's impossible to get a pixel-accurate result; in general there is no way to turn off antialiasing when drawing on a canvas and this means you will get visible see-through lines when subdividing in triangles. I also found multipass rendering working really bad on chrome (probably because of how hw-accellerated rendering is implemented).</p> <p>In general this kind of rendering is surely a stress for web browsers and apparently these use cases (strange matrices for example) are not tested very well. I was even able to get Firefox crashing so bad that it took down the whole X susbsystem on my Ubuntu.</p> <p>You can see the results of my efforts <a href="http://raksy.dyndns.org/torus.html" rel="noreferrer">here</a> or as a video <a href="http://www.youtube.com/watch?v=XHT23NnW-EY" rel="noreferrer">here</a>... IMO is surely impressing that this can be done in a browser without using 3D extensions, but I don't think current problems will be fixed in the future.</p> <p>Anyway the basic idea used to draw an image so that the 4 corners ends up in specific pixels position is to draw two triangles, each of which will use bilinear interpolation.</p> <p>In the following code I assume you have a picture object <code>texture</code> and 4 corners each of which is an object with fields <code>x,y,u,v</code> where <code>x,y</code> are pixel coordinates on the target canvas and <code>u,v</code> are pixel coordinates on <code>texture</code>:</p> <pre><code>function textureMap(ctx, texture, pts) { var tris = [[0, 1, 2], [2, 3, 0]]; // Split in two triangles for (var t=0; t&lt;2; t++) { var pp = tris[t]; var x0 = pts[pp[0]].x, x1 = pts[pp[1]].x, x2 = pts[pp[2]].x; var y0 = pts[pp[0]].y, y1 = pts[pp[1]].y, y2 = pts[pp[2]].y; var u0 = pts[pp[0]].u, u1 = pts[pp[1]].u, u2 = pts[pp[2]].u; var v0 = pts[pp[0]].v, v1 = pts[pp[1]].v, v2 = pts[pp[2]].v; // Set clipping area so that only pixels inside the triangle will // be affected by the image drawing operation ctx.save(); ctx.beginPath(); ctx.moveTo(x0, y0); ctx.lineTo(x1, y1); ctx.lineTo(x2, y2); ctx.closePath(); ctx.clip(); // Compute matrix transform var delta = u0*v1 + v0*u2 + u1*v2 - v1*u2 - v0*u1 - u0*v2; var delta_a = x0*v1 + v0*x2 + x1*v2 - v1*x2 - v0*x1 - x0*v2; var delta_b = u0*x1 + x0*u2 + u1*x2 - x1*u2 - x0*u1 - u0*x2; var delta_c = u0*v1*x2 + v0*x1*u2 + x0*u1*v2 - x0*v1*u2 - v0*u1*x2 - u0*x1*v2; var delta_d = y0*v1 + v0*y2 + y1*v2 - v1*y2 - v0*y1 - y0*v2; var delta_e = u0*y1 + y0*u2 + u1*y2 - y1*u2 - y0*u1 - u0*y2; var delta_f = u0*v1*y2 + v0*y1*u2 + y0*u1*v2 - y0*v1*u2 - v0*u1*y2 - u0*y1*v2; // Draw the transformed image ctx.transform(delta_a/delta, delta_d/delta, delta_b/delta, delta_e/delta, delta_c/delta, delta_f/delta); ctx.drawImage(texture, 0, 0); ctx.restore(); } } </code></pre> <p>Those ugly strange formulas for all those "delta" variables are used to solve two linear systems of three equations in three unknowns using <a href="http://en.wikipedia.org/wiki/Cramer&#39;s_rule" rel="noreferrer">Cramer's</a> method and <a href="http://en.wikipedia.org/wiki/Rule_of_Sarrus" rel="noreferrer">Sarrus</a> scheme for 3x3 determinants.</p> <p>More specifically we are looking for the values of <code>a</code>, <code>b</code>, ... <code>f</code> so that the following equations are satisfied</p> <pre><code>a*u0 + b*v0 + c = x0 a*u1 + b*v1 + c = x1 a*u2 + b*v2 + c = x2 d*u0 + e*v0 + f = y0 d*u1 + e*v1 + f = y1 d*u2 + e*v2 + f = y2 </code></pre> <p><code>delta</code> is the determinant of the matrix</p> <pre><code>u0 v0 1 u1 v1 1 u2 v2 1 </code></pre> <p>and for example <code>delta_a</code> is the determinant of the same matrix when you replace the first column with <code>x0</code>, <code>x1</code>, <code>x2</code>. With these you can compute <code>a = delta_a / delta</code>.</p>
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    1. COWow, your torus application is impressive... I don't mind if it's not exact on a pixel basis. Thanks for the great answer.
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    2. COOk... I'll add the texture mapping part to the answer (the source of torus.html is hard to read because I "had" to shrink it down to 4K).
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    3. COJust looked at the source and it was indeed inscrutable, very nicely done!
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