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-rw-r--r--experimental/Intersection/ConvexHull.cpp143
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diff --git a/experimental/Intersection/ConvexHull.cpp b/experimental/Intersection/ConvexHull.cpp
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-/*
- * 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 "CurveIntersection.h"
-#include "CurveUtilities.h"
-#include "IntersectionUtilities.h"
-
-/* Given a cubic, find the convex hull described by the end and control points.
- The hull may have 3 or 4 points. Cubics that degenerate into a point or line
- are not considered.
-
- The hull is computed by assuming that three points, if unique and non-linear,
- form a triangle. The fourth point may replace one of the first three, may be
- discarded if in the triangle or on an edge, or may be inserted between any of
- the three to form a convex quadralateral.
-
- The indices returned in order describe the convex hull.
-*/
-int convex_hull(const Cubic& cubic, char order[4]) {
- size_t index;
- // find top point
- size_t yMin = 0;
- for (index = 1; index < 4; ++index) {
- if (cubic[yMin].y > cubic[index].y || (cubic[yMin].y == cubic[index].y
- && cubic[yMin].x > cubic[index].x)) {
- yMin = index;
- }
- }
- order[0] = yMin;
- int midX = -1;
- int backupYMin = -1;
- for (int pass = 0; pass < 2; ++pass) {
- for (index = 0; index < 4; ++index) {
- if (index == yMin) {
- continue;
- }
- // rotate line from (yMin, index) to axis
- // see if remaining two points are both above or below
- // use this to find mid
- int mask = other_two(yMin, index);
- int side1 = yMin ^ mask;
- int side2 = index ^ mask;
- Cubic rotPath;
- if (!rotate(cubic, yMin, index, rotPath)) { // ! if cbc[yMin]==cbc[idx]
- order[1] = side1;
- order[2] = side2;
- return 3;
- }
- int sides = side(rotPath[side1].y - rotPath[yMin].y);
- sides ^= side(rotPath[side2].y - rotPath[yMin].y);
- if (sides == 2) { // '2' means one remaining point <0, one >0
- if (midX >= 0) {
- printf("%s unexpected mid\n", __FUNCTION__); // there can be only one mid
- }
- midX = index;
- } else if (sides == 0) { // '0' means both to one side or the other
- backupYMin = index;
- }
- }
- if (midX >= 0) {
- break;
- }
- if (backupYMin < 0) {
- break;
- }
- yMin = backupYMin;
- backupYMin = -1;
- }
- if (midX < 0) {
- midX = yMin ^ 3; // choose any other point
- }
- int mask = other_two(yMin, midX);
- int least = yMin ^ mask;
- int most = midX ^ mask;
- order[0] = yMin;
- order[1] = least;
-
- // see if mid value is on same side of line (least, most) as yMin
- Cubic midPath;
- if (!rotate(cubic, least, most, midPath)) { // ! if cbc[least]==cbc[most]
- order[2] = midX;
- return 3;
- }
- int midSides = side(midPath[yMin].y - midPath[least].y);
- midSides ^= side(midPath[midX].y - midPath[least].y);
- if (midSides != 2) { // if mid point is not between
- order[2] = most;
- return 3; // result is a triangle
- }
- order[2] = midX;
- order[3] = most;
- return 4; // result is a quadralateral
-}
-
-/* Find the convex hull for cubics with the x-axis interval regularly spaced.
- Cubics computed as distance functions are formed this way.
-
- connectTo0[0], connectTo0[1] are the point indices that cubic[0] connects to.
- connectTo3[0], connectTo3[1] are the point indices that cubic[3] connects to.
-
- Returns true if cubic[1] to cubic[2] also forms part of the hull.
-*/
-bool convex_x_hull(const Cubic& cubic, char connectTo0[2], char connectTo3[2]) {
- double projectedY[4];
- projectedY[0] = 0;
- int index;
- for (index = 1; index < 4; ++index) {
- projectedY[index] = (cubic[index].y - cubic[0].y) * (3.0 / index);
- }
- int lower0Index = 1;
- int upper0Index = 1;
- for (index = 2; index < 4; ++index) {
- if (approximately_greater_or_equal(projectedY[lower0Index], projectedY[index])) {
- lower0Index = index;
- }
- if (approximately_lesser_or_equal(projectedY[upper0Index], projectedY[index])) {
- upper0Index = index;
- }
- }
- connectTo0[0] = lower0Index;
- connectTo0[1] = upper0Index;
- for (index = 0; index < 3; ++index) {
- projectedY[index] = (cubic[3].y - cubic[index].y) * (3.0 / (3 - index));
- }
- projectedY[3] = 0;
- int lower3Index = 2;
- int upper3Index = 2;
- for (index = 1; index > -1; --index) {
- if (approximately_greater_or_equal(projectedY[lower3Index], projectedY[index])) {
- lower3Index = index;
- }
- if (approximately_lesser_or_equal(projectedY[upper3Index], projectedY[index])) {
- upper3Index = index;
- }
- }
- connectTo3[0] = lower3Index;
- connectTo3[1] = upper3Index;
- return (1 << lower0Index | 1 << upper0Index
- | 1 << lower3Index | 1 << upper3Index) == 0x0F;
-}