com.graphbuilder.sun.awt.geom.Curve Maven / Gradle / Ivy
Go to download
Show more of this group Show more artifacts with this name
Show all versions of curvesapi Show documentation
Show all versions of curvesapi Show documentation
Implementation of various mathematical curves that define themselves over a set of control points. The API is written in Java. The curves supported are: Bezier, B-Spline, Cardinal Spline, Catmull-Rom Spline, Lagrange, Natural Cubic Spline, and NURBS.
/*
* Copyright (c) 1998, 2006, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
package com.graphbuilder.sun.awt.geom;
import java.awt.geom.PathIterator;
import java.awt.geom.IllegalPathStateException;
public abstract class Curve {
/**
* Calculates the number of times the given path
* crosses the ray extending to the right from (px,py).
* If the point lies on a part of the path,
* then no crossings are counted for that intersection.
* +1 is added for each crossing where the Y coordinate is increasing
* -1 is added for each crossing where the Y coordinate is decreasing
* The return value is the sum of all crossings for every segment in
* the path.
* The path must start with a SEG_MOVETO, otherwise an exception is
* thrown.
* The caller must check p[xy] for NaN values.
* The caller may also reject infinite p[xy] values as well.
*/
public static int pointCrossingsForPath(PathIterator pi,
double px, double py)
{
if (pi.isDone()) {
return 0;
}
double coords[] = new double[6];
if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) {
throw new IllegalPathStateException("missing initial moveto "+
"in path definition");
}
pi.next();
double movx = coords[0];
double movy = coords[1];
double curx = movx;
double cury = movy;
double endx, endy;
int crossings = 0;
while (!pi.isDone()) {
switch (pi.currentSegment(coords)) {
case PathIterator.SEG_MOVETO:
if (cury != movy) {
crossings += pointCrossingsForLine(px, py,
curx, cury,
movx, movy);
}
movx = curx = coords[0];
movy = cury = coords[1];
break;
case PathIterator.SEG_LINETO:
endx = coords[0];
endy = coords[1];
crossings += pointCrossingsForLine(px, py,
curx, cury,
endx, endy);
curx = endx;
cury = endy;
break;
case PathIterator.SEG_QUADTO:
endx = coords[2];
endy = coords[3];
crossings += pointCrossingsForQuad(px, py,
curx, cury,
coords[0], coords[1],
endx, endy, 0);
curx = endx;
cury = endy;
break;
case PathIterator.SEG_CUBICTO:
endx = coords[4];
endy = coords[5];
crossings += pointCrossingsForCubic(px, py,
curx, cury,
coords[0], coords[1],
coords[2], coords[3],
endx, endy, 0);
curx = endx;
cury = endy;
break;
case PathIterator.SEG_CLOSE:
if (cury != movy) {
crossings += pointCrossingsForLine(px, py,
curx, cury,
movx, movy);
}
curx = movx;
cury = movy;
break;
}
pi.next();
}
if (cury != movy) {
crossings += pointCrossingsForLine(px, py,
curx, cury,
movx, movy);
}
return crossings;
}
/**
* Calculates the number of times the line from (x0,y0) to (x1,y1)
* crosses the ray extending to the right from (px,py).
* If the point lies on the line, then no crossings are recorded.
* +1 is returned for a crossing where the Y coordinate is increasing
* -1 is returned for a crossing where the Y coordinate is decreasing
*/
public static int pointCrossingsForLine(double px, double py,
double x0, double y0,
double x1, double y1)
{
if (py < y0 && py < y1) return 0;
if (py >= y0 && py >= y1) return 0;
// assert(y0 != y1);
if (px >= x0 && px >= x1) return 0;
if (px < x0 && px < x1) return (y0 < y1) ? 1 : -1;
double xintercept = x0 + (py - y0) * (x1 - x0) / (y1 - y0);
if (px >= xintercept) return 0;
return (y0 < y1) ? 1 : -1;
}
/**
* Calculates the number of times the quad from (x0,y0) to (x1,y1)
* crosses the ray extending to the right from (px,py).
* If the point lies on a part of the curve,
* then no crossings are counted for that intersection.
* the level parameter should be 0 at the top-level call and will count
* up for each recursion level to prevent infinite recursion
* +1 is added for each crossing where the Y coordinate is increasing
* -1 is added for each crossing where the Y coordinate is decreasing
*/
public static int pointCrossingsForQuad(double px, double py,
double x0, double y0,
double xc, double yc,
double x1, double y1, int level)
{
if (py < y0 && py < yc && py < y1) return 0;
if (py >= y0 && py >= yc && py >= y1) return 0;
// Note y0 could equal y1...
if (px >= x0 && px >= xc && px >= x1) return 0;
if (px < x0 && px < xc && px < x1) {
if (py >= y0) {
if (py < y1) return 1;
} else {
// py < y0
if (py >= y1) return -1;
}
// py outside of y01 range, and/or y0==y1
return 0;
}
// double precision only has 52 bits of mantissa
if (level > 52) return pointCrossingsForLine(px, py, x0, y0, x1, y1);
double x0c = (x0 + xc) / 2;
double y0c = (y0 + yc) / 2;
double xc1 = (xc + x1) / 2;
double yc1 = (yc + y1) / 2;
xc = (x0c + xc1) / 2;
yc = (y0c + yc1) / 2;
if (Double.isNaN(xc) || Double.isNaN(yc)) {
// [xy]c are NaN if any of [xy]0c or [xy]c1 are NaN
// [xy]0c or [xy]c1 are NaN if any of [xy][0c1] are NaN
// These values are also NaN if opposing infinities are added
return 0;
}
return (pointCrossingsForQuad(px, py,
x0, y0, x0c, y0c, xc, yc,
level+1) +
pointCrossingsForQuad(px, py,
xc, yc, xc1, yc1, x1, y1,
level+1));
}
/**
* Calculates the number of times the cubic from (x0,y0) to (x1,y1)
* crosses the ray extending to the right from (px,py).
* If the point lies on a part of the curve,
* then no crossings are counted for that intersection.
* the level parameter should be 0 at the top-level call and will count
* up for each recursion level to prevent infinite recursion
* +1 is added for each crossing where the Y coordinate is increasing
* -1 is added for each crossing where the Y coordinate is decreasing
*/
public static int pointCrossingsForCubic(double px, double py,
double x0, double y0,
double xc0, double yc0,
double xc1, double yc1,
double x1, double y1, int level)
{
if (py < y0 && py < yc0 && py < yc1 && py < y1) return 0;
if (py >= y0 && py >= yc0 && py >= yc1 && py >= y1) return 0;
// Note y0 could equal yc0...
if (px >= x0 && px >= xc0 && px >= xc1 && px >= x1) return 0;
if (px < x0 && px < xc0 && px < xc1 && px < x1) {
if (py >= y0) {
if (py < y1) return 1;
} else {
// py < y0
if (py >= y1) return -1;
}
// py outside of y01 range, and/or y0==yc0
return 0;
}
// double precision only has 52 bits of mantissa
if (level > 52) return pointCrossingsForLine(px, py, x0, y0, x1, y1);
double xmid = (xc0 + xc1) / 2;
double ymid = (yc0 + yc1) / 2;
xc0 = (x0 + xc0) / 2;
yc0 = (y0 + yc0) / 2;
xc1 = (xc1 + x1) / 2;
yc1 = (yc1 + y1) / 2;
double xc0m = (xc0 + xmid) / 2;
double yc0m = (yc0 + ymid) / 2;
double xmc1 = (xmid + xc1) / 2;
double ymc1 = (ymid + yc1) / 2;
xmid = (xc0m + xmc1) / 2;
ymid = (yc0m + ymc1) / 2;
if (Double.isNaN(xmid) || Double.isNaN(ymid)) {
// [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN
// [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN
// These values are also NaN if opposing infinities are added
return 0;
}
return (pointCrossingsForCubic(px, py,
x0, y0, xc0, yc0,
xc0m, yc0m, xmid, ymid, level+1) +
pointCrossingsForCubic(px, py,
xmid, ymid, xmc1, ymc1,
xc1, yc1, x1, y1, level+1));
}
/**
* The rectangle intersection test counts the number of times
* that the path crosses through the shadow that the rectangle
* projects to the right towards (x => +INFINITY).
*
* During processing of the path it actually counts every time
* the path crosses either or both of the top and bottom edges
* of that shadow. If the path enters from the top, the count
* is incremented. If it then exits back through the top, the
* same way it came in, the count is decremented and there is
* no impact on the winding count. If, instead, the path exits
* out the bottom, then the count is incremented again and a
* full pass through the shadow is indicated by the winding count
* having been incremented by 2.
*
* Thus, the winding count that it accumulates is actually double
* the real winding count. Since the path is continuous, the
* final answer should be a multiple of 2, otherwise there is a
* logic error somewhere.
*
* If the path ever has a direct hit on the rectangle, then a
* special value is returned. This special value terminates
* all ongoing accumulation on up through the call chain and
* ends up getting returned to the calling function which can
* then produce an answer directly. For intersection tests,
* the answer is always "true" if the path intersects the
* rectangle. For containment tests, the answer is always
* "false" if the path intersects the rectangle. Thus, no
* further processing is ever needed if an intersection occurs.
*/
public static final int RECT_INTERSECTS = 0x80000000;
/**
* Accumulate the number of times the path crosses the shadow
* extending to the right of the rectangle. See the comment
* for the RECT_INTERSECTS constant for more complete details.
* The return value is the sum of all crossings for both the
* top and bottom of the shadow for every segment in the path,
* or the special value RECT_INTERSECTS if the path ever enters
* the interior of the rectangle.
* The path must start with a SEG_MOVETO, otherwise an exception is
* thrown.
* The caller must check r[xy]{min,max} for NaN values.
*/
public static int rectCrossingsForPath(PathIterator pi,
double rxmin, double rymin,
double rxmax, double rymax)
{
if (rxmax <= rxmin || rymax <= rymin) {
return 0;
}
if (pi.isDone()) {
return 0;
}
double coords[] = new double[6];
if (pi.currentSegment(coords) != PathIterator.SEG_MOVETO) {
throw new IllegalPathStateException("missing initial moveto "+
"in path definition");
}
pi.next();
double curx, cury, movx, movy, endx, endy;
curx = movx = coords[0];
cury = movy = coords[1];
int crossings = 0;
while (crossings != RECT_INTERSECTS && !pi.isDone()) {
switch (pi.currentSegment(coords)) {
case PathIterator.SEG_MOVETO:
if (curx != movx || cury != movy) {
crossings = rectCrossingsForLine(crossings,
rxmin, rymin,
rxmax, rymax,
curx, cury,
movx, movy);
}
// Count should always be a multiple of 2 here.
// assert((crossings & 1) != 0);
movx = curx = coords[0];
movy = cury = coords[1];
break;
case PathIterator.SEG_LINETO:
endx = coords[0];
endy = coords[1];
crossings = rectCrossingsForLine(crossings,
rxmin, rymin,
rxmax, rymax,
curx, cury,
endx, endy);
curx = endx;
cury = endy;
break;
case PathIterator.SEG_QUADTO:
endx = coords[2];
endy = coords[3];
crossings = rectCrossingsForQuad(crossings,
rxmin, rymin,
rxmax, rymax,
curx, cury,
coords[0], coords[1],
endx, endy, 0);
curx = endx;
cury = endy;
break;
case PathIterator.SEG_CUBICTO:
endx = coords[4];
endy = coords[5];
crossings = rectCrossingsForCubic(crossings,
rxmin, rymin,
rxmax, rymax,
curx, cury,
coords[0], coords[1],
coords[2], coords[3],
endx, endy, 0);
curx = endx;
cury = endy;
break;
case PathIterator.SEG_CLOSE:
if (curx != movx || cury != movy) {
crossings = rectCrossingsForLine(crossings,
rxmin, rymin,
rxmax, rymax,
curx, cury,
movx, movy);
}
curx = movx;
cury = movy;
// Count should always be a multiple of 2 here.
// assert((crossings & 1) != 0);
break;
}
pi.next();
}
if (crossings != RECT_INTERSECTS && (curx != movx || cury != movy)) {
crossings = rectCrossingsForLine(crossings,
rxmin, rymin,
rxmax, rymax,
curx, cury,
movx, movy);
}
// Count should always be a multiple of 2 here.
// assert((crossings & 1) != 0);
return crossings;
}
/**
* Accumulate the number of times the line crosses the shadow
* extending to the right of the rectangle. See the comment
* for the RECT_INTERSECTS constant for more complete details.
*/
public static int rectCrossingsForLine(int crossings,
double rxmin, double rymin,
double rxmax, double rymax,
double x0, double y0,
double x1, double y1)
{
if (y0 >= rymax && y1 >= rymax) return crossings;
if (y0 <= rymin && y1 <= rymin) return crossings;
if (x0 <= rxmin && x1 <= rxmin) return crossings;
if (x0 >= rxmax && x1 >= rxmax) {
// Line is entirely to the right of the rect
// and the vertical ranges of the two overlap by a non-empty amount
// Thus, this line segment is partially in the "right-shadow"
// Path may have done a complete crossing
// Or path may have entered or exited the right-shadow
if (y0 < y1) {
// y-increasing line segment...
// We know that y0 < rymax and y1 > rymin
if (y0 <= rymin) crossings++;
if (y1 >= rymax) crossings++;
} else if (y1 < y0) {
// y-decreasing line segment...
// We know that y1 < rymax and y0 > rymin
if (y1 <= rymin) crossings--;
if (y0 >= rymax) crossings--;
}
return crossings;
}
// Remaining case:
// Both x and y ranges overlap by a non-empty amount
// First do trivial INTERSECTS rejection of the cases
// where one of the endpoints is inside the rectangle.
if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) ||
(x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax))
{
return RECT_INTERSECTS;
}
// Otherwise calculate the y intercepts and see where
// they fall with respect to the rectangle
double xi0 = x0;
if (y0 < rymin) {
xi0 += ((rymin - y0) * (x1 - x0) / (y1 - y0));
} else if (y0 > rymax) {
xi0 += ((rymax - y0) * (x1 - x0) / (y1 - y0));
}
double xi1 = x1;
if (y1 < rymin) {
xi1 += ((rymin - y1) * (x0 - x1) / (y0 - y1));
} else if (y1 > rymax) {
xi1 += ((rymax - y1) * (x0 - x1) / (y0 - y1));
}
if (xi0 <= rxmin && xi1 <= rxmin) return crossings;
if (xi0 >= rxmax && xi1 >= rxmax) {
if (y0 < y1) {
// y-increasing line segment...
// We know that y0 < rymax and y1 > rymin
if (y0 <= rymin) crossings++;
if (y1 >= rymax) crossings++;
} else if (y1 < y0) {
// y-decreasing line segment...
// We know that y1 < rymax and y0 > rymin
if (y1 <= rymin) crossings--;
if (y0 >= rymax) crossings--;
}
return crossings;
}
return RECT_INTERSECTS;
}
/**
* Accumulate the number of times the quad crosses the shadow
* extending to the right of the rectangle. See the comment
* for the RECT_INTERSECTS constant for more complete details.
*/
public static int rectCrossingsForQuad(int crossings,
double rxmin, double rymin,
double rxmax, double rymax,
double x0, double y0,
double xc, double yc,
double x1, double y1,
int level)
{
if (y0 >= rymax && yc >= rymax && y1 >= rymax) return crossings;
if (y0 <= rymin && yc <= rymin && y1 <= rymin) return crossings;
if (x0 <= rxmin && xc <= rxmin && x1 <= rxmin) return crossings;
if (x0 >= rxmax && xc >= rxmax && x1 >= rxmax) {
// Quad is entirely to the right of the rect
// and the vertical range of the 3 Y coordinates of the quad
// overlaps the vertical range of the rect by a non-empty amount
// We now judge the crossings solely based on the line segment
// connecting the endpoints of the quad.
// Note that we may have 0, 1, or 2 crossings as the control
// point may be causing the Y range intersection while the
// two endpoints are entirely above or below.
if (y0 < y1) {
// y-increasing line segment...
if (y0 <= rymin && y1 > rymin) crossings++;
if (y0 < rymax && y1 >= rymax) crossings++;
} else if (y1 < y0) {
// y-decreasing line segment...
if (y1 <= rymin && y0 > rymin) crossings--;
if (y1 < rymax && y0 >= rymax) crossings--;
}
return crossings;
}
// The intersection of ranges is more complicated
// First do trivial INTERSECTS rejection of the cases
// where one of the endpoints is inside the rectangle.
if ((x0 < rxmax && x0 > rxmin && y0 < rymax && y0 > rymin) ||
(x1 < rxmax && x1 > rxmin && y1 < rymax && y1 > rymin))
{
return RECT_INTERSECTS;
}
// Otherwise, subdivide and look for one of the cases above.
// double precision only has 52 bits of mantissa
if (level > 52) {
return rectCrossingsForLine(crossings,
rxmin, rymin, rxmax, rymax,
x0, y0, x1, y1);
}
double x0c = (x0 + xc) / 2;
double y0c = (y0 + yc) / 2;
double xc1 = (xc + x1) / 2;
double yc1 = (yc + y1) / 2;
xc = (x0c + xc1) / 2;
yc = (y0c + yc1) / 2;
if (Double.isNaN(xc) || Double.isNaN(yc)) {
// [xy]c are NaN if any of [xy]0c or [xy]c1 are NaN
// [xy]0c or [xy]c1 are NaN if any of [xy][0c1] are NaN
// These values are also NaN if opposing infinities are added
return 0;
}
crossings = rectCrossingsForQuad(crossings,
rxmin, rymin, rxmax, rymax,
x0, y0, x0c, y0c, xc, yc,
level+1);
if (crossings != RECT_INTERSECTS) {
crossings = rectCrossingsForQuad(crossings,
rxmin, rymin, rxmax, rymax,
xc, yc, xc1, yc1, x1, y1,
level+1);
}
return crossings;
}
/**
* Accumulate the number of times the cubic crosses the shadow
* extending to the right of the rectangle. See the comment
* for the RECT_INTERSECTS constant for more complete details.
*/
public static int rectCrossingsForCubic(int crossings,
double rxmin, double rymin,
double rxmax, double rymax,
double x0, double y0,
double xc0, double yc0,
double xc1, double yc1,
double x1, double y1,
int level)
{
if (y0 >= rymax && yc0 >= rymax && yc1 >= rymax && y1 >= rymax) {
return crossings;
}
if (y0 <= rymin && yc0 <= rymin && yc1 <= rymin && y1 <= rymin) {
return crossings;
}
if (x0 <= rxmin && xc0 <= rxmin && xc1 <= rxmin && x1 <= rxmin) {
return crossings;
}
if (x0 >= rxmax && xc0 >= rxmax && xc1 >= rxmax && x1 >= rxmax) {
// Cubic is entirely to the right of the rect
// and the vertical range of the 4 Y coordinates of the cubic
// overlaps the vertical range of the rect by a non-empty amount
// We now judge the crossings solely based on the line segment
// connecting the endpoints of the cubic.
// Note that we may have 0, 1, or 2 crossings as the control
// points may be causing the Y range intersection while the
// two endpoints are entirely above or below.
if (y0 < y1) {
// y-increasing line segment...
if (y0 <= rymin && y1 > rymin) crossings++;
if (y0 < rymax && y1 >= rymax) crossings++;
} else if (y1 < y0) {
// y-decreasing line segment...
if (y1 <= rymin && y0 > rymin) crossings--;
if (y1 < rymax && y0 >= rymax) crossings--;
}
return crossings;
}
// The intersection of ranges is more complicated
// First do trivial INTERSECTS rejection of the cases
// where one of the endpoints is inside the rectangle.
if ((x0 > rxmin && x0 < rxmax && y0 > rymin && y0 < rymax) ||
(x1 > rxmin && x1 < rxmax && y1 > rymin && y1 < rymax))
{
return RECT_INTERSECTS;
}
// Otherwise, subdivide and look for one of the cases above.
// double precision only has 52 bits of mantissa
if (level > 52) {
return rectCrossingsForLine(crossings,
rxmin, rymin, rxmax, rymax,
x0, y0, x1, y1);
}
double xmid = (xc0 + xc1) / 2;
double ymid = (yc0 + yc1) / 2;
xc0 = (x0 + xc0) / 2;
yc0 = (y0 + yc0) / 2;
xc1 = (xc1 + x1) / 2;
yc1 = (yc1 + y1) / 2;
double xc0m = (xc0 + xmid) / 2;
double yc0m = (yc0 + ymid) / 2;
double xmc1 = (xmid + xc1) / 2;
double ymc1 = (ymid + yc1) / 2;
xmid = (xc0m + xmc1) / 2;
ymid = (yc0m + ymc1) / 2;
if (Double.isNaN(xmid) || Double.isNaN(ymid)) {
// [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN
// [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN
// These values are also NaN if opposing infinities are added
return 0;
}
crossings = rectCrossingsForCubic(crossings,
rxmin, rymin, rxmax, rymax,
x0, y0, xc0, yc0,
xc0m, yc0m, xmid, ymid, level+1);
if (crossings != RECT_INTERSECTS) {
crossings = rectCrossingsForCubic(crossings,
rxmin, rymin, rxmax, rymax,
xmid, ymid, xmc1, ymc1,
xc1, yc1, x1, y1, level+1);
}
return crossings;
}
}
© 2015 - 2025 Weber Informatics LLC | Privacy Policy