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[Impeller] Use Wang's formula for quad/cubic subdivision. #52079
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,53 @@ | ||
| // Copyright 2013 The Flutter Authors. All rights reserved. | ||
| // Use of this source code is governed by a BSD-style license that can be | ||
| // found in the LICENSE file. | ||
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| #include "impeller/geometry/wangs_formula.h" | ||
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| namespace impeller { | ||
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| namespace { | ||
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| // Don't allow linearized segments to be off by more than 1/4th of a pixel from | ||
| // the true curve. This value should be scaled by the max basis of the | ||
| // X and Y directions. | ||
| constexpr static Scalar kPrecision = 4; | ||
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| constexpr Scalar length(Point n) { | ||
| Point nn = n * n; | ||
| return std::sqrt(nn.x + nn.y); | ||
| } | ||
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| } // namespace | ||
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| Scalar ComputeCubicSubdivisions(Scalar scale_factor, | ||
| Point p0, | ||
| Point p1, | ||
| Point p2, | ||
| Point p3) { | ||
| Scalar k = scale_factor * .75f * kPrecision; | ||
| Point a = (p0 - p1 * 2 + p2).Abs(); | ||
| Point b = (p1 - p2 * 2 + p3).Abs(); | ||
| return std::sqrt(k * length(a.Max(b))); | ||
| } | ||
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| Scalar ComputeQuadradicSubdivisions(Scalar scale_factor, | ||
| Point p0, | ||
| Point p1, | ||
| Point p2) { | ||
| Scalar k = scale_factor * .25f * kPrecision; | ||
| return std::sqrt(k * length(p0 - p1 * 2 + p2)); | ||
| } | ||
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| Scalar ComputeQuadradicSubdivisions(Scalar scale_factor, | ||
| const QuadraticPathComponent& quad) { | ||
| return ComputeQuadradicSubdivisions(scale_factor, quad.p1, quad.cp, quad.p2); | ||
| } | ||
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| Scalar ComputeCubicSubdivisions(float scale_factor, | ||
| const CubicPathComponent& cub) { | ||
| return ComputeCubicSubdivisions(scale_factor, cub.p1, cub.cp1, cub.cp2, | ||
| cub.p2); | ||
| } | ||
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| } // namespace impeller |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,65 @@ | ||
| // Copyright 2013 The Flutter Authors. All rights reserved. | ||
| // Use of this source code is governed by a BSD-style license that can be | ||
| // found in the LICENSE file. | ||
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| #ifndef FLUTTER_IMPELLER_GEOMETRY_WANGS_FORMULA_H_ | ||
| #define FLUTTER_IMPELLER_GEOMETRY_WANGS_FORMULA_H_ | ||
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| #include "impeller/geometry/path_component.h" | ||
| #include "impeller/geometry/point.h" | ||
| #include "impeller/geometry/scalar.h" | ||
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| // Skia GPU Ports | ||
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| // Wang's formula gives the minimum number of evenly spaced (in the parametric | ||
| // sense) line segments that a bezier curve must be chopped into in order to | ||
| // guarantee all lines stay within a distance of "1/precision" pixels from the | ||
| // true curve. Its definition for a bezier curve of degree "n" is as follows: | ||
| // | ||
| // maxLength = max([length(p[i+2] - 2p[i+1] + p[i]) for (0 <= i <= n-2)]) | ||
| // numParametricSegments = sqrt(maxLength * precision * n*(n - 1)/8) | ||
| // | ||
| // (Goldman, Ron. (2003). 5.6.3 Wang's Formula. "Pyramid Algorithms: A Dynamic | ||
| // Programming Approach to Curves and Surfaces for Geometric Modeling". Morgan | ||
| // Kaufmann Publishers.) | ||
| namespace impeller { | ||
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| /// Returns the minimum number of evenly spaced (in the parametric sense) line | ||
| /// segments that the cubic must be chopped into in order to guarantee all lines | ||
| /// stay within a distance of "1/intolerance" pixels from the true curve. | ||
| /// | ||
| /// The scale_factor should be the max basis XY of the current transform. | ||
| Scalar ComputeCubicSubdivisions(Scalar scale_factor, | ||
| Point p0, | ||
| Point p1, | ||
| Point p2, | ||
| Point p3); | ||
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| /// Returns the minimum number of evenly spaced (in the parametric sense) line | ||
| /// segments that the quadratic must be chopped into in order to guarantee all | ||
| /// lines stay within a distance of "1/intolerance" pixels from the true curve. | ||
| /// | ||
| /// The scale_factor should be the max basis XY of the current transform. | ||
| Scalar ComputeQuadradicSubdivisions(Scalar scale_factor, | ||
| Point p0, | ||
| Point p1, | ||
| Point p2); | ||
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| /// Returns the minimum number of evenly spaced (in the parametric sense) line | ||
| /// segments that the quadratic must be chopped into in order to guarantee all | ||
| /// lines stay within a distance of "1/intolerance" pixels from the true curve. | ||
| /// | ||
| /// The scale_factor should be the max basis XY of the current transform. | ||
| Scalar ComputeQuadradicSubdivisions(Scalar scale_factor, | ||
| const QuadraticPathComponent& quad); | ||
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| /// Returns the minimum number of evenly spaced (in the parametric sense) line | ||
| /// segments that the cubic must be chopped into in order to guarantee all lines | ||
| /// stay within a distance of "1/intolerance" pixels from the true curve. | ||
| /// | ||
| /// The scale_factor should be the max basis XY of the current transform. | ||
| Scalar ComputeCubicSubdivisions(float scale_factor, | ||
| const CubicPathComponent& cub); | ||
| } // namespace impeller | ||
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| #endif // FLUTTER_IMPELLER_GEOMETRY_WANGS_FORMULA_H_ |
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This is testing a case that no longer matters since we don't use the tessellator. i suspect it broke because we're now generating fewer line segments, since our cubic division isn't as cranky.
As a follow up I plan to delete most of this code.