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-rw-r--r--experimental/Intersection/ReduceOrder.cpp238
1 files changed, 0 insertions, 238 deletions
diff --git a/experimental/Intersection/ReduceOrder.cpp b/experimental/Intersection/ReduceOrder.cpp
deleted file mode 100644
index e742a265e0..0000000000
--- a/experimental/Intersection/ReduceOrder.cpp
+++ /dev/null
@@ -1,238 +0,0 @@
-#include "CubicIntersection.h"
-#include "Extrema.h"
-#include "IntersectionUtilities.h"
-#include "LineParameters.h"
-
-#ifdef MAYBE_USEFUL_IN_THE_FUTURE
-static double interp_quad_coords(double a, double b, double c, double t)
-{
- double ab = interp(a, b, t);
- double bc = interp(b, c, t);
- return interp(ab, bc, t);
-}
-#endif
-
-static double interp_cubic_coords(const double* src, double t)
-{
- double ab = interp(src[0], src[2], t);
- double bc = interp(src[2], src[4], t);
- double cd = interp(src[4], src[6], t);
- double abc = interp(ab, bc, t);
- double bcd = interp(bc, cd, t);
- return interp(abc, bcd, t);
-}
-
-static int coincident_line(const Cubic& cubic, Cubic& reduction) {
- reduction[0] = reduction[1] = cubic[0];
- return 1;
-}
-
-static int vertical_line(const Cubic& cubic, Cubic& reduction) {
- double tValues[2];
- reduction[0] = cubic[0];
- reduction[1] = cubic[3];
- int smaller = reduction[1].y > reduction[0].y;
- int larger = smaller ^ 1;
- int roots = SkFindCubicExtrema(cubic[0].y, cubic[1].y, cubic[2].y, cubic[3].y, tValues);
- for (int index = 0; index < roots; ++index) {
- double yExtrema = interp_cubic_coords(&cubic[0].y, tValues[index]);
- if (reduction[smaller].y > yExtrema) {
- reduction[smaller].y = yExtrema;
- continue;
- }
- if (reduction[larger].y < yExtrema) {
- reduction[larger].y = yExtrema;
- }
- }
- return 2;
-}
-
-static int horizontal_line(const Cubic& cubic, Cubic& reduction) {
- double tValues[2];
- reduction[0] = cubic[0];
- reduction[1] = cubic[3];
- int smaller = reduction[1].x > reduction[0].x;
- int larger = smaller ^ 1;
- int roots = SkFindCubicExtrema(cubic[0].x, cubic[1].x, cubic[2].x, cubic[3].x, tValues);
- for (int index = 0; index < roots; ++index) {
- double xExtrema = interp_cubic_coords(&cubic[0].x, tValues[index]);
- if (reduction[smaller].x > xExtrema) {
- reduction[smaller].x = xExtrema;
- continue;
- }
- if (reduction[larger].x < xExtrema) {
- reduction[larger].x = xExtrema;
- }
- }
- return 2;
-}
-
-// check to see if it is a quadratic or a line
-static int check_quadratic(const Cubic& cubic, Cubic& reduction,
- int minX, int maxX, int minY, int maxY) {
- double dx10 = cubic[1].x - cubic[0].x;
- double dx23 = cubic[2].x - cubic[3].x;
- double midX = cubic[0].x + dx10 * 3 / 2;
- if (!approximately_equal(midX - cubic[3].x, dx23 * 3 / 2)) {
- return 0;
- }
- double dy10 = cubic[1].y - cubic[0].y;
- double dy23 = cubic[2].y - cubic[3].y;
- double midY = cubic[0].y + dy10 * 3 / 2;
- if (!approximately_equal(midY - cubic[3].y, dy23 * 3 / 2)) {
- return 0;
- }
- reduction[0] = cubic[0];
- reduction[1].x = midX;
- reduction[1].y = midY;
- reduction[2] = cubic[3];
- return 3;
-}
-
-static int check_linear(const Cubic& cubic, Cubic& reduction,
- int minX, int maxX, int minY, int maxY) {
- int startIndex = 0;
- int endIndex = 3;
- while (cubic[startIndex].approximatelyEqual(cubic[endIndex])) {
- --endIndex;
- if (endIndex == 0) {
- printf("%s shouldn't get here if all four points are about equal", __FUNCTION__);
- assert(0);
- }
- }
- LineParameters lineParameters;
- lineParameters.cubicEndPoints(cubic, startIndex, endIndex);
- double normalSquared = lineParameters.normalSquared();
- double distance[2]; // distance is not normalized
- int mask = other_two(startIndex, endIndex);
- int inner1 = startIndex ^ mask;
- int inner2 = endIndex ^ mask;
- lineParameters.controlPtDistance(cubic, inner1, inner2, distance);
- double limit = normalSquared * SquaredEpsilon;
- int index;
- for (index = 0; index < 2; ++index) {
- double distSq = distance[index];
- distSq *= distSq;
- if (distSq > limit) {
- return 0;
- }
- }
- // four are colinear: return line formed by outside
- reduction[0] = cubic[0];
- reduction[1] = cubic[3];
- int sameSide1;
- int sameSide2;
- bool useX = cubic[maxX].x - cubic[minX].x >= cubic[maxY].y - cubic[minY].y;
- if (useX) {
- sameSide1 = sign(cubic[0].x - cubic[1].x) + sign(cubic[3].x - cubic[1].x);
- sameSide2 = sign(cubic[0].x - cubic[2].x) + sign(cubic[3].x - cubic[2].x);
- } else {
- sameSide1 = sign(cubic[0].y - cubic[1].y) + sign(cubic[3].y - cubic[1].y);
- sameSide2 = sign(cubic[0].y - cubic[2].y) + sign(cubic[3].y - cubic[2].y);
- }
- if (sameSide1 == sameSide2 && (sameSide1 & 3) != 2) {
- return 2;
- }
- double tValues[2];
- int roots;
- if (useX) {
- roots = SkFindCubicExtrema(cubic[0].x, cubic[1].x, cubic[2].x, cubic[3].x, tValues);
- } else {
- roots = SkFindCubicExtrema(cubic[0].y, cubic[1].y, cubic[2].y, cubic[3].y, tValues);
- }
- for (index = 0; index < roots; ++index) {
- _Point extrema;
- extrema.x = interp_cubic_coords(&cubic[0].x, tValues[index]);
- extrema.y = interp_cubic_coords(&cubic[0].y, tValues[index]);
- // sameSide > 0 means mid is smaller than either [0] or [3], so replace smaller
- int replace;
- if (useX) {
- if (extrema.x < cubic[0].x ^ extrema.x < cubic[3].x) {
- continue;
- }
- replace = (extrema.x < cubic[0].x | extrema.x < cubic[3].x)
- ^ cubic[0].x < cubic[3].x;
- } else {
- if (extrema.y < cubic[0].y ^ extrema.y < cubic[3].y) {
- continue;
- }
- replace = (extrema.y < cubic[0].y | extrema.y < cubic[3].y)
- ^ cubic[0].y < cubic[3].y;
- }
- reduction[replace] = extrema;
- }
- return 2;
-}
-
-/* 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 reduceOrder(const Cubic& cubic, Cubic& reduction, ReduceOrder_Flags 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].x > cubic[index].x) {
- minX = index;
- }
- if (cubic[minY].y > cubic[index].y) {
- minY = index;
- }
- if (cubic[maxX].x < cubic[index].x) {
- maxX = index;
- }
- if (cubic[maxY].y < cubic[index].y) {
- maxY = index;
- }
- }
- for (index = 0; index < 4; ++index) {
- if (approximately_equal(cubic[index].x, cubic[minX].x)) {
- minXSet |= 1 << index;
- }
- if (approximately_equal(cubic[index].y, cubic[minY].y)) {
- minYSet |= 1 << index;
- }
- }
- if (minXSet == 0xF) { // test for vertical line
- if (minYSet == 0xF) { // return 1 if all four are coincident
- return coincident_line(cubic, reduction);
- }
- return vertical_line(cubic, reduction);
- }
- if (minYSet == 0xF) { // test for horizontal line
- return horizontal_line(cubic, reduction);
- }
- int result = check_linear(cubic, reduction, minX, maxX, minY, maxY);
- if (result) {
- return result;
- }
- if (allowQuadratics && (result = check_quadratic(cubic, reduction, minX, maxX, minY, maxY))) {
- return result;
- }
- memcpy(reduction, cubic, sizeof(Cubic));
- return 4;
-}
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