| /* |
| * Copyright 2014 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| #include "SkPatchUtils.h" |
| |
| #include "SkColorPriv.h" |
| #include "SkGeometry.h" |
| |
| /** |
| * Evaluator to sample the values of a cubic bezier using forward differences. |
| * Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only |
| * adding precalculated values. |
| * For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h |
| * would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first |
| * evaluation f(t) then we need to substract f(t+h) - f(t) = m*t + m*h + b - m*t + b = mh. After |
| * obtaining this value (mh) we could just add this constant step to our first sampled point |
| * to compute the next one. |
| * |
| * For the cubic case the first difference gives as a result a quadratic polynomial to which we can |
| * apply again forward differences and get linear function to which we can apply again forward |
| * differences to get a constant difference. This is why we keep an array of size 4, the 0th |
| * position keeps the sampled value while the next ones keep the quadratic, linear and constant |
| * difference values. |
| */ |
| |
| class FwDCubicEvaluator { |
| |
| public: |
| |
| /** |
| * Receives the 4 control points of the cubic bezier. |
| */ |
| |
| explicit FwDCubicEvaluator(const SkPoint points[4]) |
| : fCoefs(points) { |
| memcpy(fPoints, points, 4 * sizeof(SkPoint)); |
| |
| this->restart(1); |
| } |
| |
| /** |
| * Restarts the forward differences evaluator to the first value of t = 0. |
| */ |
| void restart(int divisions) { |
| fDivisions = divisions; |
| fCurrent = 0; |
| fMax = fDivisions + 1; |
| Sk2s h = Sk2s(1.f / fDivisions); |
| Sk2s h2 = h * h; |
| Sk2s h3 = h2 * h; |
| Sk2s fwDiff3 = Sk2s(6) * fCoefs.fA * h3; |
| fFwDiff[3] = to_point(fwDiff3); |
| fFwDiff[2] = to_point(fwDiff3 + times_2(fCoefs.fB) * h2); |
| fFwDiff[1] = to_point(fCoefs.fA * h3 + fCoefs.fB * h2 + fCoefs.fC * h); |
| fFwDiff[0] = to_point(fCoefs.fD); |
| } |
| |
| /** |
| * Check if the evaluator is still within the range of 0<=t<=1 |
| */ |
| bool done() const { |
| return fCurrent > fMax; |
| } |
| |
| /** |
| * Call next to obtain the SkPoint sampled and move to the next one. |
| */ |
| SkPoint next() { |
| SkPoint point = fFwDiff[0]; |
| fFwDiff[0] += fFwDiff[1]; |
| fFwDiff[1] += fFwDiff[2]; |
| fFwDiff[2] += fFwDiff[3]; |
| fCurrent++; |
| return point; |
| } |
| |
| const SkPoint* getCtrlPoints() const { |
| return fPoints; |
| } |
| |
| private: |
| SkCubicCoeff fCoefs; |
| int fMax, fCurrent, fDivisions; |
| SkPoint fFwDiff[4], fPoints[4]; |
| }; |
| |
| //////////////////////////////////////////////////////////////////////////////// |
| |
| // size in pixels of each partition per axis, adjust this knob |
| static const int kPartitionSize = 10; |
| |
| /** |
| * Calculate the approximate arc length given a bezier curve's control points. |
| */ |
| static SkScalar approx_arc_length(SkPoint* points, int count) { |
| if (count < 2) { |
| return 0; |
| } |
| SkScalar arcLength = 0; |
| for (int i = 0; i < count - 1; i++) { |
| arcLength += SkPoint::Distance(points[i], points[i + 1]); |
| } |
| return arcLength; |
| } |
| |
| static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01, |
| SkScalar c11) { |
| SkScalar a = c00 * (1.f - tx) + c10 * tx; |
| SkScalar b = c01 * (1.f - tx) + c11 * tx; |
| return a * (1.f - ty) + b * ty; |
| } |
| |
| SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) { |
| |
| // Approximate length of each cubic. |
| SkPoint pts[kNumPtsCubic]; |
| SkPatchUtils::getTopCubic(cubics, pts); |
| matrix->mapPoints(pts, kNumPtsCubic); |
| SkScalar topLength = approx_arc_length(pts, kNumPtsCubic); |
| |
| SkPatchUtils::getBottomCubic(cubics, pts); |
| matrix->mapPoints(pts, kNumPtsCubic); |
| SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic); |
| |
| SkPatchUtils::getLeftCubic(cubics, pts); |
| matrix->mapPoints(pts, kNumPtsCubic); |
| SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic); |
| |
| SkPatchUtils::getRightCubic(cubics, pts); |
| matrix->mapPoints(pts, kNumPtsCubic); |
| SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic); |
| |
| // Level of detail per axis, based on the larger side between top and bottom or left and right |
| int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize); |
| int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize); |
| |
| return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY)); |
| } |
| |
| void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) { |
| points[0] = cubics[kTopP0_CubicCtrlPts]; |
| points[1] = cubics[kTopP1_CubicCtrlPts]; |
| points[2] = cubics[kTopP2_CubicCtrlPts]; |
| points[3] = cubics[kTopP3_CubicCtrlPts]; |
| } |
| |
| void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) { |
| points[0] = cubics[kBottomP0_CubicCtrlPts]; |
| points[1] = cubics[kBottomP1_CubicCtrlPts]; |
| points[2] = cubics[kBottomP2_CubicCtrlPts]; |
| points[3] = cubics[kBottomP3_CubicCtrlPts]; |
| } |
| |
| void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) { |
| points[0] = cubics[kLeftP0_CubicCtrlPts]; |
| points[1] = cubics[kLeftP1_CubicCtrlPts]; |
| points[2] = cubics[kLeftP2_CubicCtrlPts]; |
| points[3] = cubics[kLeftP3_CubicCtrlPts]; |
| } |
| |
| void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) { |
| points[0] = cubics[kRightP0_CubicCtrlPts]; |
| points[1] = cubics[kRightP1_CubicCtrlPts]; |
| points[2] = cubics[kRightP2_CubicCtrlPts]; |
| points[3] = cubics[kRightP3_CubicCtrlPts]; |
| } |
| |
| bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12], |
| const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) { |
| if (lodX < 1 || lodY < 1 || nullptr == cubics || nullptr == data) { |
| return false; |
| } |
| |
| // check for overflow in multiplication |
| const int64_t lodX64 = (lodX + 1), |
| lodY64 = (lodY + 1), |
| mult64 = lodX64 * lodY64; |
| if (mult64 > SK_MaxS32) { |
| return false; |
| } |
| data->fVertexCount = SkToS32(mult64); |
| |
| // it is recommended to generate draw calls of no more than 65536 indices, so we never generate |
| // more than 60000 indices. To accomplish that we resize the LOD and vertex count |
| if (data->fVertexCount > 10000 || lodX > 200 || lodY > 200) { |
| SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY); |
| SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY); |
| |
| // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of |
| // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6) |
| lodX = static_cast<int>(weightX * 200); |
| lodY = static_cast<int>(weightY * 200); |
| data->fVertexCount = (lodX + 1) * (lodY + 1); |
| } |
| data->fIndexCount = lodX * lodY * 6; |
| |
| data->fPoints = new SkPoint[data->fVertexCount]; |
| data->fIndices = new uint16_t[data->fIndexCount]; |
| |
| // if colors is not null then create array for colors |
| SkPMColor colorsPM[kNumCorners]; |
| if (colors) { |
| // premultiply colors to avoid color bleeding. |
| for (int i = 0; i < kNumCorners; i++) { |
| colorsPM[i] = SkPreMultiplyColor(colors[i]); |
| } |
| data->fColors = new uint32_t[data->fVertexCount]; |
| } |
| |
| // if texture coordinates are not null then create array for them |
| if (texCoords) { |
| data->fTexCoords = new SkPoint[data->fVertexCount]; |
| } |
| |
| SkPoint pts[kNumPtsCubic]; |
| SkPatchUtils::getBottomCubic(cubics, pts); |
| FwDCubicEvaluator fBottom(pts); |
| SkPatchUtils::getTopCubic(cubics, pts); |
| FwDCubicEvaluator fTop(pts); |
| SkPatchUtils::getLeftCubic(cubics, pts); |
| FwDCubicEvaluator fLeft(pts); |
| SkPatchUtils::getRightCubic(cubics, pts); |
| FwDCubicEvaluator fRight(pts); |
| |
| fBottom.restart(lodX); |
| fTop.restart(lodX); |
| |
| SkScalar u = 0.0f; |
| int stride = lodY + 1; |
| for (int x = 0; x <= lodX; x++) { |
| SkPoint bottom = fBottom.next(), top = fTop.next(); |
| fLeft.restart(lodY); |
| fRight.restart(lodY); |
| SkScalar v = 0.f; |
| for (int y = 0; y <= lodY; y++) { |
| int dataIndex = x * (lodY + 1) + y; |
| |
| SkPoint left = fLeft.next(), right = fRight.next(); |
| |
| SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(), |
| (1.0f - v) * top.y() + v * bottom.y()); |
| SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(), |
| (1.0f - u) * left.y() + u * right.y()); |
| SkPoint s2 = SkPoint::Make( |
| (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x() |
| + u * fTop.getCtrlPoints()[3].x()) |
| + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x() |
| + u * fBottom.getCtrlPoints()[3].x()), |
| (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y() |
| + u * fTop.getCtrlPoints()[3].y()) |
| + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y() |
| + u * fBottom.getCtrlPoints()[3].y())); |
| data->fPoints[dataIndex] = s0 + s1 - s2; |
| |
| if (colors) { |
| uint8_t a = uint8_t(bilerp(u, v, |
| SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])), |
| SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])), |
| SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])), |
| SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner])))); |
| uint8_t r = uint8_t(bilerp(u, v, |
| SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])), |
| SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])), |
| SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])), |
| SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner])))); |
| uint8_t g = uint8_t(bilerp(u, v, |
| SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])), |
| SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])), |
| SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])), |
| SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner])))); |
| uint8_t b = uint8_t(bilerp(u, v, |
| SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])), |
| SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])), |
| SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])), |
| SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner])))); |
| data->fColors[dataIndex] = SkPackARGB32(a,r,g,b); |
| } |
| |
| if (texCoords) { |
| data->fTexCoords[dataIndex] = SkPoint::Make( |
| bilerp(u, v, texCoords[kTopLeft_Corner].x(), |
| texCoords[kTopRight_Corner].x(), |
| texCoords[kBottomLeft_Corner].x(), |
| texCoords[kBottomRight_Corner].x()), |
| bilerp(u, v, texCoords[kTopLeft_Corner].y(), |
| texCoords[kTopRight_Corner].y(), |
| texCoords[kBottomLeft_Corner].y(), |
| texCoords[kBottomRight_Corner].y())); |
| |
| } |
| |
| if(x < lodX && y < lodY) { |
| int i = 6 * (x * lodY + y); |
| data->fIndices[i] = x * stride + y; |
| data->fIndices[i + 1] = x * stride + 1 + y; |
| data->fIndices[i + 2] = (x + 1) * stride + 1 + y; |
| data->fIndices[i + 3] = data->fIndices[i]; |
| data->fIndices[i + 4] = data->fIndices[i + 2]; |
| data->fIndices[i + 5] = (x + 1) * stride + y; |
| } |
| v = SkScalarClampMax(v + 1.f / lodY, 1); |
| } |
| u = SkScalarClampMax(u + 1.f / lodX, 1); |
| } |
| return true; |
| |
| } |