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https://github.com/italicsjenga/vello.git
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Fancy flattening
Implement same flattening algorithm as kurbo.
This commit is contained in:
Raph Levien
parent
eaa1d261c3
commit
79cc9da811
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@ -34,14 +34,65 @@ layout(set = 0, binding = 2) buffer TileBuf {
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#define SY (1.0 / float(TILE_HEIGHT_PX))
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#define ACCURACY 0.25
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#define Q_ACCURACY 0.01
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#define Q_ACCURACY (ACCURACY * 0.1)
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#define REM_ACCURACY (ACCURACY - Q_ACCURACY)
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#define MAX_HYPOT2 (432.0 * Q_ACCURACY * Q_ACCURACY)
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vec2 eval_quad(vec2 p0, vec2 p1, vec2 p2, float t) {
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float mt = 1.0 - t;
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return p0 * (mt * mt) + (p1 * (mt * 2.0) + p2 * t) * t;
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}
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vec2 eval_cubic(vec2 p0, vec2 p1, vec2 p2, vec2 p3, float t) {
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float mt = 1.0 - t;
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return p0 * (mt * mt * mt) + (p1 * (mt * mt * 3.0) + (p2 * (mt * 3.0) + p3 * t) * t) * t;
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}
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struct SubdivResult {
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float val;
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float a0;
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float a2;
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};
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/// An approximation to $\int (1 + 4x^2) ^ -0.25 dx$
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///
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/// This is used for flattening curves.
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#define D 0.67
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float approx_parabola_integral(float x) {
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return x * inversesqrt(sqrt(1.0 - D + (D * D * D * D + 0.25 * x * x)));
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}
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/// An approximation to the inverse parabola integral.
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#define B 0.39
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float approx_parabola_inv_integral(float x) {
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return x * sqrt(1.0 - B + (B * B + 0.25 * x * x));
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}
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SubdivResult estimate_subdiv(vec2 p0, vec2 p1, vec2 p2, float sqrt_tol) {
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vec2 d01 = p1 - p0;
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vec2 d12 = p2 - p1;
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vec2 dd = d01 - d12;
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float cross = (p2.x - p0.x) * dd.y - (p2.y - p0.y) * dd.x;
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float x0 = (d01.x * dd.x + d01.y * dd.y) / cross;
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float x2 = (d12.x * dd.x + d12.y * dd.y) / cross;
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float scale = abs(cross / (length(dd) * (x2 - x0)));
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float a0 = approx_parabola_integral(x0);
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float a2 = approx_parabola_integral(x2);
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float val = 0.0;
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if (scale < 1e9) {
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float da = abs(a2 - a0);
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float sqrt_scale = sqrt(scale);
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if (sign(x0) == sign(x2)) {
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val = da * sqrt_scale;
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} else {
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float xmin = sqrt_tol / sqrt_scale;
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val = sqrt_tol * da / approx_parabola_integral(xmin);
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}
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}
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return SubdivResult(val, a0, a2);
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}
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void main() {
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uint element_ix = gl_GlobalInvocationID.x;
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PathSegRef ref = PathSegRef(element_ix * PathSeg_size);
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@ -78,35 +129,63 @@ void main() {
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case PathSeg_StrokeCubic:
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PathStrokeCubic cubic = PathSeg_StrokeCubic_read(ref);
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// Commented out code is for computing error bound on conversion to quadratics
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/*
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vec2 err_v = 3.0 * (cubic.p2 - cubic.p1) + cubic.p0 - cubic.p3;
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float err = err_v.x * err_v.x + err_v.y * err_v.y;
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// The number of quadratics.
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uint n = max(uint(ceil(pow(err * (1.0 / MAX_HYPOT2), 1.0 / 6.0))), 1);
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*/
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// This calculation is based on Sederberg, CAGD Notes section 10.6
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vec2 l = max(abs(cubic.p0 + cubic.p2 - 2 * cubic.p1), abs(cubic.p1 + cubic.p3 - 2 * cubic.p2));
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uint n = max(uint(ceil(sqrt(length(l) * (0.75 / ACCURACY)))), 1);
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vec2 p0 = cubic.p0;
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float step = 1.0 / float(n);
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uint n_quads = max(uint(ceil(pow(err * (1.0 / MAX_HYPOT2), 1.0 / 6.0))), 1);
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// Iterate over quadratics and tote up the estimated number of segments.
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float val = 0.0;
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vec2 qp0 = cubic.p0;
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float step = 1.0 / float(n_quads);
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for (uint i = 0; i < n_quads; i++) {
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float t = float(i + 1) * step;
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vec2 qp2 = eval_cubic(cubic.p0, cubic.p1, cubic.p2, cubic.p3, t);
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vec2 qp1 = eval_cubic(cubic.p0, cubic.p1, cubic.p2, cubic.p3, t - 0.5 * step);
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qp1 = 2.0 * qp1 - 0.5 * (qp0 + qp2);
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SubdivResult params = estimate_subdiv(qp0, qp1, qp2, sqrt(REM_ACCURACY));
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val += params.val;
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qp0 = qp2;
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}
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uint n = max(uint(ceil(val * 0.5 / sqrt(REM_ACCURACY))), 1);
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uint path_ix = cubic.path_ix;
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Path path = Path_read(PathRef(path_ix * Path_size));
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ivec4 bbox = ivec4(path.bbox);
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for (int i = 0; i < n; i++) {
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// TODO: probably need special logic to make sure it's manifold
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vec2 p0 = cubic.p0;
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qp0 = cubic.p0;
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float v_step = val / float(n);
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int n_out = 1;
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float val_sum = 0.0;
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for (uint i = 0; i < n_quads; i++) {
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float t = float(i + 1) * step;
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vec2 p2 = eval_cubic(cubic.p0, cubic.p1, cubic.p2, cubic.p3, t);
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/*
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vec2 p1 = eval_cubic(cubic.p0, cubic.p1, cubic.p2, cubic.p3, t - 0.5 * step);
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p1 = 2.0 * p1 - 0.5 * (p0 + p2);
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*/
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vec2 qp2 = eval_cubic(cubic.p0, cubic.p1, cubic.p2, cubic.p3, t);
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vec2 qp1 = eval_cubic(cubic.p0, cubic.p1, cubic.p2, cubic.p3, t - 0.5 * step);
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qp1 = 2.0 * qp1 - 0.5 * (qp0 + qp2);
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SubdivResult params = estimate_subdiv(qp0, qp1, qp2, sqrt(REM_ACCURACY));
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float u0 = approx_parabola_inv_integral(params.a0);
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float u2 = approx_parabola_inv_integral(params.a2);
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float uscale = 1.0 / (u2 - u0);
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float target = float(n_out) * v_step;
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while (n_out == n || target < val_sum + params.val) {
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vec2 p1;
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if (n_out == n) {
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p1 = cubic.p3;
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} else {
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float u = (target - val_sum) / params.val;
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float a = mix(params.a0, params.a2, u);
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float au = approx_parabola_inv_integral(a);
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float t = (au - u0) * uscale;
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p1 = eval_quad(qp0, qp1, qp2, t);
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}
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xmin = min(p0.x, p2.x) - cubic.stroke.x;
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xmax = max(p0.x, p2.x) + cubic.stroke.x;
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ymin = min(p0.y, p2.y) - cubic.stroke.y;
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ymax = max(p0.y, p2.y) + cubic.stroke.y;
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float dx = p2.x - p0.x;
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float dy = p2.y - p0.y;
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// Output line segment
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xmin = min(p0.x, p1.x) - cubic.stroke.x;
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xmax = max(p0.x, p1.x) + cubic.stroke.x;
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ymin = min(p0.y, p1.y) - cubic.stroke.y;
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ymax = max(p0.y, p1.y) + cubic.stroke.y;
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float dx = p1.x - p0.x;
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float dy = p1.y - p0.y;
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// Set up for per-scanline coverage formula, below.
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float invslope = abs(dy) < 1e-9 ? 1e9 : dx / dy;
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c = (cubic.stroke.x + abs(invslope) * (0.5 * float(TILE_HEIGHT_PX) + cubic.stroke.y)) * SX;
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@ -132,10 +211,10 @@ void main() {
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TileSeg tile_seg;
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for (int y = y0; y < y1; y++) {
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float tile_y0 = float(y * TILE_HEIGHT_PX);
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if (tag == PathSeg_FillCubic && min(p0.y, p2.y) <= tile_y0) {
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if (tag == PathSeg_FillCubic && min(p0.y, p1.y) <= tile_y0) {
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int xray = max(int(ceil(xc - 0.5 * b)), bbox.x);
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if (xray < bbox.z) {
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int backdrop = p2.y < p0.y ? 1 : -1;
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int backdrop = p1.y < p0.y ? 1 : -1;
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TileRef tile_ref = Tile_index(path.tiles, uint(base + xray));
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uint tile_el = tile_ref.offset >> 2;
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atomicAdd(tile[tile_el + 1], backdrop);
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@ -149,12 +228,12 @@ void main() {
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uint tile_el = tile_ref.offset >> 2;
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uint old = atomicExchange(tile[tile_el], tile_offset);
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tile_seg.start = p0;
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tile_seg.end = p2;
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tile_seg.end = p1;
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float y_edge = 0.0;
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if (tag == PathSeg_FillCubic) {
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y_edge = mix(p0.y, p2.y, (tile_x0 - p0.x) / dx);
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if (min(p0.x, p2.x) < tile_x0 && y_edge >= tile_y0 && y_edge < tile_y0 + TILE_HEIGHT_PX) {
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if (p0.x > p2.x) {
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y_edge = mix(p0.y, p1.y, (tile_x0 - p0.x) / dx);
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if (min(p0.x, p1.x) < tile_x0 && y_edge >= tile_y0 && y_edge < tile_y0 + TILE_HEIGHT_PX) {
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if (p0.x > p1.x) {
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tile_seg.end = vec2(tile_x0, y_edge);
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} else {
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tile_seg.start = vec2(tile_x0, y_edge);
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@ -172,8 +251,15 @@ void main() {
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base += stride;
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}
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p0 = p2;
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n_out += 1;
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target += v_step;
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p0 = p1;
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}
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val_sum += params.val;
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qp0 = qp2;
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}
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break;
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}
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}
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