/*
* 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:
FwDCubicEvaluator()
: fMax(0)
, fCurrent(0)
, fDivisions(0) {
memset(fPoints, 0, 4 * sizeof(SkPoint));
memset(fPoints, 0, 4 * sizeof(SkPoint));
memset(fPoints, 0, 4 * sizeof(SkPoint));
}
/**
* Receives the 4 control points of the cubic bezier.
*/
FwDCubicEvaluator(SkPoint a, SkPoint b, SkPoint c, SkPoint d) {
fPoints[0] = a;
fPoints[1] = b;
fPoints[2] = c;
fPoints[3] = d;
SkCubicToCoeff(fPoints, fCoefs);
this->restart(1);
}
explicit FwDCubicEvaluator(const SkPoint points[4]) {
memcpy(fPoints, points, 4 * sizeof(SkPoint));
SkCubicToCoeff(fPoints, fCoefs);
this->restart(1);
}
/**
* Restarts the forward differences evaluator to the first value of t = 0.
*/
void restart(int divisions) {
fDivisions = divisions;
SkScalar h = 1.f / fDivisions;
fCurrent = 0;
fMax = fDivisions + 1;
fFwDiff[0] = fCoefs[3];
SkScalar h2 = h * h;
SkScalar h3 = h2 * h;
fFwDiff[3].set(6.f * fCoefs[0].x() * h3, 6.f * fCoefs[0].y() * h3); //6ah^3
fFwDiff[2].set(fFwDiff[3].x() + 2.f * fCoefs[1].x() * h2, //6ah^3 + 2bh^2
fFwDiff[3].y() + 2.f * fCoefs[1].y() * h2);
fFwDiff[1].set(fCoefs[0].x() * h3 + fCoefs[1].x() * h2 + fCoefs[2].x() * h,//ah^3 + bh^2 +ch
fCoefs[0].y() * h3 + fCoefs[1].y() * h2 + fCoefs[2].y() * h);
}
/**
* 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:
int fMax, fCurrent, fDivisions;
SkPoint fFwDiff[4], fCoefs[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 || NULL == cubics || NULL == 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 = SkNEW_ARRAY(SkPoint, data->fVertexCount);
data->fIndices = SkNEW_ARRAY(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 = SkNEW_ARRAY(uint32_t, data->fVertexCount);
}
// if texture coordinates are not null then create array for them
if (texCoords) {
data->fTexCoords = SkNEW_ARRAY(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;
}