b45a1b46ee
git-svn-id: http://skia.googlecode.com/svn/trunk@4006 2bbb7eff-a529-9590-31e7-b0007b416f81
237 lines
7.9 KiB
C++
237 lines
7.9 KiB
C++
#include "CurveIntersection.h"
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#include "Extrema.h"
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#include "IntersectionUtilities.h"
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#include "LineParameters.h"
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static double interp_cubic_coords(const double* src, double t)
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{
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double ab = interp(src[0], src[2], t);
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double bc = interp(src[2], src[4], t);
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double cd = interp(src[4], src[6], t);
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double abc = interp(ab, bc, t);
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double bcd = interp(bc, cd, t);
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return interp(abc, bcd, t);
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}
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static int coincident_line(const Cubic& cubic, Cubic& reduction) {
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reduction[0] = reduction[1] = cubic[0];
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return 1;
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}
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static int vertical_line(const Cubic& cubic, Cubic& reduction) {
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double tValues[2];
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reduction[0] = cubic[0];
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reduction[1] = cubic[3];
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int smaller = reduction[1].y > reduction[0].y;
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int larger = smaller ^ 1;
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int roots = findExtrema(cubic[0].y, cubic[1].y, cubic[2].y, cubic[3].y, tValues);
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for (int index = 0; index < roots; ++index) {
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double yExtrema = interp_cubic_coords(&cubic[0].y, tValues[index]);
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if (reduction[smaller].y > yExtrema) {
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reduction[smaller].y = yExtrema;
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continue;
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}
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if (reduction[larger].y < yExtrema) {
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reduction[larger].y = yExtrema;
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}
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}
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return 2;
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}
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static int horizontal_line(const Cubic& cubic, Cubic& reduction) {
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double tValues[2];
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reduction[0] = cubic[0];
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reduction[1] = cubic[3];
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int smaller = reduction[1].x > reduction[0].x;
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int larger = smaller ^ 1;
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int roots = findExtrema(cubic[0].x, cubic[1].x, cubic[2].x, cubic[3].x, tValues);
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for (int index = 0; index < roots; ++index) {
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double xExtrema = interp_cubic_coords(&cubic[0].x, tValues[index]);
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if (reduction[smaller].x > xExtrema) {
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reduction[smaller].x = xExtrema;
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continue;
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}
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if (reduction[larger].x < xExtrema) {
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reduction[larger].x = xExtrema;
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}
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}
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return 2;
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}
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// check to see if it is a quadratic or a line
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static int check_quadratic(const Cubic& cubic, Cubic& reduction,
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int minX, int maxX, int minY, int maxY) {
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double dx10 = cubic[1].x - cubic[0].x;
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double dx23 = cubic[2].x - cubic[3].x;
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double midX = cubic[0].x + dx10 * 3 / 2;
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if (!approximately_equal(midX - cubic[3].x, dx23 * 3 / 2)) {
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return 0;
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}
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double dy10 = cubic[1].y - cubic[0].y;
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double dy23 = cubic[2].y - cubic[3].y;
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double midY = cubic[0].y + dy10 * 3 / 2;
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if (!approximately_equal(midY - cubic[3].y, dy23 * 3 / 2)) {
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return 0;
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}
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reduction[0] = cubic[0];
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reduction[1].x = midX;
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reduction[1].y = midY;
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reduction[2] = cubic[3];
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return 3;
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}
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static int check_linear(const Cubic& cubic, Cubic& reduction,
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int minX, int maxX, int minY, int maxY) {
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int startIndex = 0;
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int endIndex = 3;
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while (cubic[startIndex].approximatelyEqual(cubic[endIndex])) {
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--endIndex;
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if (endIndex == 0) {
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printf("%s shouldn't get here if all four points are about equal", __FUNCTION__);
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assert(0);
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}
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}
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if (!isLinear(cubic, startIndex, endIndex)) {
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return 0;
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}
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// four are colinear: return line formed by outside
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reduction[0] = cubic[0];
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reduction[1] = cubic[3];
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int sameSide1;
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int sameSide2;
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bool useX = cubic[maxX].x - cubic[minX].x >= cubic[maxY].y - cubic[minY].y;
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if (useX) {
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sameSide1 = sign(cubic[0].x - cubic[1].x) + sign(cubic[3].x - cubic[1].x);
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sameSide2 = sign(cubic[0].x - cubic[2].x) + sign(cubic[3].x - cubic[2].x);
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} else {
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sameSide1 = sign(cubic[0].y - cubic[1].y) + sign(cubic[3].y - cubic[1].y);
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sameSide2 = sign(cubic[0].y - cubic[2].y) + sign(cubic[3].y - cubic[2].y);
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}
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if (sameSide1 == sameSide2 && (sameSide1 & 3) != 2) {
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return 2;
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}
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double tValues[2];
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int roots;
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if (useX) {
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roots = findExtrema(cubic[0].x, cubic[1].x, cubic[2].x, cubic[3].x, tValues);
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} else {
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roots = findExtrema(cubic[0].y, cubic[1].y, cubic[2].y, cubic[3].y, tValues);
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}
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for (int index = 0; index < roots; ++index) {
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_Point extrema;
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extrema.x = interp_cubic_coords(&cubic[0].x, tValues[index]);
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extrema.y = interp_cubic_coords(&cubic[0].y, tValues[index]);
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// sameSide > 0 means mid is smaller than either [0] or [3], so replace smaller
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int replace;
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if (useX) {
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if (extrema.x < cubic[0].x ^ extrema.x < cubic[3].x) {
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continue;
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}
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replace = (extrema.x < cubic[0].x | extrema.x < cubic[3].x)
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^ cubic[0].x < cubic[3].x;
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} else {
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if (extrema.y < cubic[0].y ^ extrema.y < cubic[3].y) {
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continue;
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}
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replace = (extrema.y < cubic[0].y | extrema.y < cubic[3].y)
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^ cubic[0].y < cubic[3].y;
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}
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reduction[replace] = extrema;
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}
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return 2;
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}
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bool isLinear(const Cubic& cubic, int startIndex, int endIndex) {
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LineParameters lineParameters;
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lineParameters.cubicEndPoints(cubic, startIndex, endIndex);
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double normalSquared = lineParameters.normalSquared();
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double distance[2]; // distance is not normalized
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int mask = other_two(startIndex, endIndex);
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int inner1 = startIndex ^ mask;
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int inner2 = endIndex ^ mask;
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lineParameters.controlPtDistance(cubic, inner1, inner2, distance);
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double limit = normalSquared;
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int index;
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for (index = 0; index < 2; ++index) {
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double distSq = distance[index];
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distSq *= distSq;
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if (approximately_greater(distSq, limit)) {
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return false;
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}
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}
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return true;
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}
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/* food for thought:
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http://objectmix.com/graphics/132906-fast-precision-driven-cubic-quadratic-piecewise-degree-reduction-algos-2-a.html
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Given points c1, c2, c3 and c4 of a cubic Bezier, the points of the
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corresponding quadratic Bezier are (given in convex combinations of
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points):
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q1 = (11/13)c1 + (3/13)c2 -(3/13)c3 + (2/13)c4
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q2 = -c1 + (3/2)c2 + (3/2)c3 - c4
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q3 = (2/13)c1 - (3/13)c2 + (3/13)c3 + (11/13)c4
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Of course, this curve does not interpolate the end-points, but it would
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be interesting to see the behaviour of such a curve in an applet.
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--
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Kalle Rutanen
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http://kaba.hilvi.org
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*/
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// reduce to a quadratic or smaller
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// look for identical points
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// look for all four points in a line
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// note that three points in a line doesn't simplify a cubic
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// look for approximation with single quadratic
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// save approximation with multiple quadratics for later
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int reduceOrder(const Cubic& cubic, Cubic& reduction, ReduceOrder_Flags allowQuadratics) {
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int index, minX, maxX, minY, maxY;
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int minXSet, minYSet;
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minX = maxX = minY = maxY = 0;
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minXSet = minYSet = 0;
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for (index = 1; index < 4; ++index) {
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if (cubic[minX].x > cubic[index].x) {
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minX = index;
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}
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if (cubic[minY].y > cubic[index].y) {
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minY = index;
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}
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if (cubic[maxX].x < cubic[index].x) {
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maxX = index;
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}
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if (cubic[maxY].y < cubic[index].y) {
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maxY = index;
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}
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}
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for (index = 0; index < 4; ++index) {
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if (approximately_equal(cubic[index].x, cubic[minX].x)) {
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minXSet |= 1 << index;
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}
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if (approximately_equal(cubic[index].y, cubic[minY].y)) {
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minYSet |= 1 << index;
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}
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}
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if (minXSet == 0xF) { // test for vertical line
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if (minYSet == 0xF) { // return 1 if all four are coincident
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return coincident_line(cubic, reduction);
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}
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return vertical_line(cubic, reduction);
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}
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if (minYSet == 0xF) { // test for horizontal line
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return horizontal_line(cubic, reduction);
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}
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int result = check_linear(cubic, reduction, minX, maxX, minY, maxY);
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if (result) {
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return result;
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}
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if (allowQuadratics && (result = check_quadratic(cubic, reduction, minX, maxX, minY, maxY))) {
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return result;
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}
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memcpy(reduction, cubic, sizeof(Cubic));
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return 4;
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}
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