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 /* * 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(SkMaxScalar(topLength, bottomLength) / kPartitionSize); int lodY = static_cast(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(lodX) / (lodX + lodY); SkScalar weightY = static_cast(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(weightX * 200); lodY = static_cast(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; }