/*
|
* Copyright 2012 Google Inc.
|
*
|
* Use of this source code is governed by a BSD-style license that can be
|
* found in the LICENSE file.
|
*/
|
#include "SkGeometry.h"
|
#include "SkReduceOrder.h"
|
|
int SkReduceOrder::reduce(const SkDLine& line) {
|
fLine[0] = line[0];
|
int different = line[0] != line[1];
|
fLine[1] = line[different];
|
return 1 + different;
|
}
|
|
static int coincident_line(const SkDQuad& quad, SkDQuad& reduction) {
|
reduction[0] = reduction[1] = quad[0];
|
return 1;
|
}
|
|
static int reductionLineCount(const SkDQuad& reduction) {
|
return 1 + !reduction[0].approximatelyEqual(reduction[1]);
|
}
|
|
static int vertical_line(const SkDQuad& quad, SkDQuad& reduction) {
|
reduction[0] = quad[0];
|
reduction[1] = quad[2];
|
return reductionLineCount(reduction);
|
}
|
|
static int horizontal_line(const SkDQuad& quad, SkDQuad& reduction) {
|
reduction[0] = quad[0];
|
reduction[1] = quad[2];
|
return reductionLineCount(reduction);
|
}
|
|
static int check_linear(const SkDQuad& quad,
|
int minX, int maxX, int minY, int maxY, SkDQuad& reduction) {
|
if (!quad.isLinear(0, 2)) {
|
return 0;
|
}
|
// four are colinear: return line formed by outside
|
reduction[0] = quad[0];
|
reduction[1] = quad[2];
|
return reductionLineCount(reduction);
|
}
|
|
// reduce to a quadratic or smaller
|
// look for identical points
|
// look for all four points in a line
|
// note that three points in a line doesn't simplify a cubic
|
// look for approximation with single quadratic
|
// save approximation with multiple quadratics for later
|
int SkReduceOrder::reduce(const SkDQuad& quad) {
|
int index, minX, maxX, minY, maxY;
|
int minXSet, minYSet;
|
minX = maxX = minY = maxY = 0;
|
minXSet = minYSet = 0;
|
for (index = 1; index < 3; ++index) {
|
if (quad[minX].fX > quad[index].fX) {
|
minX = index;
|
}
|
if (quad[minY].fY > quad[index].fY) {
|
minY = index;
|
}
|
if (quad[maxX].fX < quad[index].fX) {
|
maxX = index;
|
}
|
if (quad[maxY].fY < quad[index].fY) {
|
maxY = index;
|
}
|
}
|
for (index = 0; index < 3; ++index) {
|
if (AlmostEqualUlps(quad[index].fX, quad[minX].fX)) {
|
minXSet |= 1 << index;
|
}
|
if (AlmostEqualUlps(quad[index].fY, quad[minY].fY)) {
|
minYSet |= 1 << index;
|
}
|
}
|
if ((minXSet & 0x05) == 0x5 && (minYSet & 0x05) == 0x5) { // test for degenerate
|
// this quad starts and ends at the same place, so never contributes
|
// to the fill
|
return coincident_line(quad, fQuad);
|
}
|
if (minXSet == 0x7) { // test for vertical line
|
return vertical_line(quad, fQuad);
|
}
|
if (minYSet == 0x7) { // test for horizontal line
|
return horizontal_line(quad, fQuad);
|
}
|
int result = check_linear(quad, minX, maxX, minY, maxY, fQuad);
|
if (result) {
|
return result;
|
}
|
fQuad = quad;
|
return 3;
|
}
|
|
////////////////////////////////////////////////////////////////////////////////////
|
|
static int coincident_line(const SkDCubic& cubic, SkDCubic& reduction) {
|
reduction[0] = reduction[1] = cubic[0];
|
return 1;
|
}
|
|
static int reductionLineCount(const SkDCubic& reduction) {
|
return 1 + !reduction[0].approximatelyEqual(reduction[1]);
|
}
|
|
static int vertical_line(const SkDCubic& cubic, SkDCubic& reduction) {
|
reduction[0] = cubic[0];
|
reduction[1] = cubic[3];
|
return reductionLineCount(reduction);
|
}
|
|
static int horizontal_line(const SkDCubic& cubic, SkDCubic& reduction) {
|
reduction[0] = cubic[0];
|
reduction[1] = cubic[3];
|
return reductionLineCount(reduction);
|
}
|
|
// check to see if it is a quadratic or a line
|
static int check_quadratic(const SkDCubic& cubic, SkDCubic& reduction) {
|
double dx10 = cubic[1].fX - cubic[0].fX;
|
double dx23 = cubic[2].fX - cubic[3].fX;
|
double midX = cubic[0].fX + dx10 * 3 / 2;
|
double sideAx = midX - cubic[3].fX;
|
double sideBx = dx23 * 3 / 2;
|
if (approximately_zero(sideAx) ? !approximately_equal(sideAx, sideBx)
|
: !AlmostEqualUlps_Pin(sideAx, sideBx)) {
|
return 0;
|
}
|
double dy10 = cubic[1].fY - cubic[0].fY;
|
double dy23 = cubic[2].fY - cubic[3].fY;
|
double midY = cubic[0].fY + dy10 * 3 / 2;
|
double sideAy = midY - cubic[3].fY;
|
double sideBy = dy23 * 3 / 2;
|
if (approximately_zero(sideAy) ? !approximately_equal(sideAy, sideBy)
|
: !AlmostEqualUlps_Pin(sideAy, sideBy)) {
|
return 0;
|
}
|
reduction[0] = cubic[0];
|
reduction[1].fX = midX;
|
reduction[1].fY = midY;
|
reduction[2] = cubic[3];
|
return 3;
|
}
|
|
static int check_linear(const SkDCubic& cubic,
|
int minX, int maxX, int minY, int maxY, SkDCubic& reduction) {
|
if (!cubic.isLinear(0, 3)) {
|
return 0;
|
}
|
// four are colinear: return line formed by outside
|
reduction[0] = cubic[0];
|
reduction[1] = cubic[3];
|
return reductionLineCount(reduction);
|
}
|
|
/* food for thought:
|
http://objectmix.com/graphics/132906-fast-precision-driven-cubic-quadratic-piecewise-degree-reduction-algos-2-a.html
|
|
Given points c1, c2, c3 and c4 of a cubic Bezier, the points of the
|
corresponding quadratic Bezier are (given in convex combinations of
|
points):
|
|
q1 = (11/13)c1 + (3/13)c2 -(3/13)c3 + (2/13)c4
|
q2 = -c1 + (3/2)c2 + (3/2)c3 - c4
|
q3 = (2/13)c1 - (3/13)c2 + (3/13)c3 + (11/13)c4
|
|
Of course, this curve does not interpolate the end-points, but it would
|
be interesting to see the behaviour of such a curve in an applet.
|
|
--
|
Kalle Rutanen
|
http://kaba.hilvi.org
|
|
*/
|
|
// reduce to a quadratic or smaller
|
// look for identical points
|
// look for all four points in a line
|
// note that three points in a line doesn't simplify a cubic
|
// look for approximation with single quadratic
|
// save approximation with multiple quadratics for later
|
int SkReduceOrder::reduce(const SkDCubic& cubic, Quadratics allowQuadratics) {
|
int index, minX, maxX, minY, maxY;
|
int minXSet, minYSet;
|
minX = maxX = minY = maxY = 0;
|
minXSet = minYSet = 0;
|
for (index = 1; index < 4; ++index) {
|
if (cubic[minX].fX > cubic[index].fX) {
|
minX = index;
|
}
|
if (cubic[minY].fY > cubic[index].fY) {
|
minY = index;
|
}
|
if (cubic[maxX].fX < cubic[index].fX) {
|
maxX = index;
|
}
|
if (cubic[maxY].fY < cubic[index].fY) {
|
maxY = index;
|
}
|
}
|
for (index = 0; index < 4; ++index) {
|
double cx = cubic[index].fX;
|
double cy = cubic[index].fY;
|
double denom = SkTMax(fabs(cx), SkTMax(fabs(cy),
|
SkTMax(fabs(cubic[minX].fX), fabs(cubic[minY].fY))));
|
if (denom == 0) {
|
minXSet |= 1 << index;
|
minYSet |= 1 << index;
|
continue;
|
}
|
double inv = 1 / denom;
|
if (approximately_equal_half(cx * inv, cubic[minX].fX * inv)) {
|
minXSet |= 1 << index;
|
}
|
if (approximately_equal_half(cy * inv, cubic[minY].fY * inv)) {
|
minYSet |= 1 << index;
|
}
|
}
|
if (minXSet == 0xF) { // test for vertical line
|
if (minYSet == 0xF) { // return 1 if all four are coincident
|
return coincident_line(cubic, fCubic);
|
}
|
return vertical_line(cubic, fCubic);
|
}
|
if (minYSet == 0xF) { // test for horizontal line
|
return horizontal_line(cubic, fCubic);
|
}
|
int result = check_linear(cubic, minX, maxX, minY, maxY, fCubic);
|
if (result) {
|
return result;
|
}
|
if (allowQuadratics == SkReduceOrder::kAllow_Quadratics
|
&& (result = check_quadratic(cubic, fCubic))) {
|
return result;
|
}
|
fCubic = cubic;
|
return 4;
|
}
|
|
SkPath::Verb SkReduceOrder::Quad(const SkPoint a[3], SkPoint* reducePts) {
|
SkDQuad quad;
|
quad.set(a);
|
SkReduceOrder reducer;
|
int order = reducer.reduce(quad);
|
if (order == 2) { // quad became line
|
for (int index = 0; index < order; ++index) {
|
*reducePts++ = reducer.fLine[index].asSkPoint();
|
}
|
}
|
return SkPathOpsPointsToVerb(order - 1);
|
}
|
|
SkPath::Verb SkReduceOrder::Conic(const SkConic& c, SkPoint* reducePts) {
|
SkPath::Verb verb = SkReduceOrder::Quad(c.fPts, reducePts);
|
if (verb > SkPath::kLine_Verb && c.fW == 1) {
|
return SkPath::kQuad_Verb;
|
}
|
return verb == SkPath::kQuad_Verb ? SkPath::kConic_Verb : verb;
|
}
|
|
SkPath::Verb SkReduceOrder::Cubic(const SkPoint a[4], SkPoint* reducePts) {
|
if (SkDPoint::ApproximatelyEqual(a[0], a[1]) && SkDPoint::ApproximatelyEqual(a[0], a[2])
|
&& SkDPoint::ApproximatelyEqual(a[0], a[3])) {
|
reducePts[0] = a[0];
|
return SkPath::kMove_Verb;
|
}
|
SkDCubic cubic;
|
cubic.set(a);
|
SkReduceOrder reducer;
|
int order = reducer.reduce(cubic, kAllow_Quadratics);
|
if (order == 2 || order == 3) { // cubic became line or quad
|
for (int index = 0; index < order; ++index) {
|
*reducePts++ = reducer.fQuad[index].asSkPoint();
|
}
|
}
|
return SkPathOpsPointsToVerb(order - 1);
|
}
|
