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Some more documentation for in the rasterizer #182

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Some more documentation for in the rasterizer #182

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29 changes: 17 additions & 12 deletions src/rasterizer.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -135,7 +135,7 @@ pub struct ActiveEdge {
// Shift is used to "scale" how fast we move along the quadratic curve.
// The key is that we scale dx and dy by the same amount so it doesn't need to have a physical unit
// as long as it doesn't overshoot.
// shift isdiv_fixed16_fixed16 probably also needed to balance number of bits that we need and make sure we don't
// shift is probably also needed to balance number of bits that we need and make sure we don't
// overflow the 32 bits we have.
// It looks like some of quantities are stored in a "sliding fixed point" representation where the
// point depends on the shift.
Expand Down Expand Up @@ -358,13 +358,16 @@ impl Rasterizer {
self.bounds_right = self.bounds_right.max(dot2_to_int(edge.control_x + 3));

// Based on Skia
// we'll iterate t from 0..1 (0-256)
// range of A is 4 times coordinate-range
// We'll iterate via forward difference.
// The second derivative is constant over the quadratic curve. We evaluate the derivative
// (the slope) at each step by adding the second derivative to the slope of the previous step.
// Similarly, the new position can be evaluated by adding the slope to the previous position.
// The range of A is 4 times coordinate-range
// we can get more accuracy here by using the input points instead of the rounded versions
// A is derived from `dot2_to_dot16(2 * (from - 2 * ctrl + to))`, it is the second derivative of the
// quadratic bézier.
let mut A = (edge.x1 - edge.control_x - edge.control_x + edge.x2) << (15 - SAMPLE_SHIFT);
let mut B = edge.control_x - edge.x1; // The derivative at the start of the curve is 2 * (ctrl - from).
let A = (edge.x1 - edge.control_x - edge.control_x + edge.x2) << (15 - SAMPLE_SHIFT);
let B = 2 * (edge.control_x - edge.x1); // The derivative at the start of the curve.
//let mut C = edge.x1;
let mut shift = compute_curve_steps(&edge);

Expand All @@ -375,19 +378,19 @@ impl Rasterizer {
}
e.shift = shift;
e.count = 1 << shift;
e.dx = 2 * (A >> shift) + 2 * B * (1 << (16 - SAMPLE_SHIFT));
e.dx = 2 * (A >> shift) + dot2_to_dot16(B);
e.ddx = 2 * (A >> (shift - 1));

A = (edge.y1 - edge.control_y - edge.control_y + edge.y2) << (15 - SAMPLE_SHIFT);
B = edge.control_y - edge.y1;
let A = (edge.y1 - edge.control_y - edge.control_y + edge.y2) << (15 - SAMPLE_SHIFT);
let B = 2 * (edge.control_y - edge.y1);
//C = edge.y1;
e.dy = 2 * (A >> shift) + 2 * B * (1 << (16 - SAMPLE_SHIFT));
e.dy = 2 * (A >> shift) + dot2_to_dot16(B);

@nical nical Mar 30, 2022

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Note: the skia equivalent looks simpler: https://github.com/RazrFalcon/tiny-skia/blob/afa3172310bb7a30e44911ef825f06dd900a4d85/src/edge.rs#L234 (note the comment above about preserving a bit by not multiplying by two and compensating in the curve shift).

e.ddy = 2 * (A >> (shift - 1));

// compute the first next_x,y
e.count -= 1;
e.next_x = (e.fullx) + (e.dx >> e.shift);
e.next_y = (cury * (1 << (16 - SAMPLE_SHIFT))) + (e.dy >> e.shift);
e.next_y = dot2_to_dot16(cury) + (e.dy >> e.shift);
e.dx += e.ddx;
e.dy += e.ddy;

Expand All @@ -403,10 +406,12 @@ impl Rasterizer {
e.next_y = dot2_to_dot16(edge.y2);
e.next_x = dot2_to_dot16(edge.x2);
}
e.slope_x = (e.next_x - (e.fullx)) / dot16_to_dot2(e.next_y - dot2_to_dot16(cury));
e.slope_x = (e.next_x - e.fullx) / dot16_to_dot2(e.next_y - dot2_to_dot16(cury));
} else {
e.shift = 0;
e.slope_x = (edge.x2 - edge.x1) * (1 << (16 - SAMPLE_SHIFT)) / (edge.y2 - edge.y1);
// We do `dot2_to_dot16(a)/b` instead of `dot2_to_dot16(a / b)` to sacrifice
// higher bits instead of lower ones.
e.slope_x = dot2_to_dot16(edge.x2 - edge.x1) / (edge.y2 - edge.y1);
}

if cury < 0 {
Expand Down