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modules/javafx.graphics/src/main/java/com/sun/marlin/Curve.java
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@@ -1,7 +1,7 @@
/*
- * Copyright (c) 2007, 2017, Oracle and/or its affiliates. All rights reserved.
+ * Copyright (c) 2007, 2018, 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
@@ -31,113 +31,132 @@
float dax, day, dbx, dby;
Curve() {
}
- void set(float[] points, int type) {
- switch(type) {
- case 8:
+ void set(final float[] points, final int type) {
+ // if instead of switch (perf + most probable cases first)
+ if (type == 8) {
set(points[0], points[1],
points[2], points[3],
points[4], points[5],
points[6], points[7]);
- return;
- case 6:
+ } else if (type == 4) {
+ set(points[0], points[1],
+ points[2], points[3]);
+ } else {
set(points[0], points[1],
points[2], points[3],
points[4], points[5]);
- return;
- default:
- throw new InternalError("Curves can only be cubic or quadratic");
}
}
- void set(float x1, float y1,
- float x2, float y2,
- float x3, float y3,
- float x4, float y4)
+ void set(final float x1, final float y1,
+ final float x2, final float y2,
+ final float x3, final float y3,
+ final float x4, final float y4)
{
final float dx32 = 3.0f * (x3 - x2);
final float dy32 = 3.0f * (y3 - y2);
final float dx21 = 3.0f * (x2 - x1);
final float dy21 = 3.0f * (y2 - y1);
- ax = (x4 - x1) - dx32;
+ ax = (x4 - x1) - dx32; // A = P3 - P0 - 3 (P2 - P1) = (P3 - P0) + 3 (P1 - P2)
ay = (y4 - y1) - dy32;
- bx = (dx32 - dx21);
+ bx = (dx32 - dx21); // B = 3 (P2 - P1) - 3(P1 - P0) = 3 (P2 + P0) - 6 P1
by = (dy32 - dy21);
- cx = dx21;
+ cx = dx21; // C = 3 (P1 - P0)
cy = dy21;
- dx = x1;
+ dx = x1; // D = P0
dy = y1;
- dax = 3.0f * ax; day = 3.0f * ay;
- dbx = 2.0f * bx; dby = 2.0f * by;
+ dax = 3.0f * ax;
+ day = 3.0f * ay;
+ dbx = 2.0f * bx;
+ dby = 2.0f * by;
}
- void set(float x1, float y1,
- float x2, float y2,
- float x3, float y3)
+ void set(final float x1, final float y1,
+ final float x2, final float y2,
+ final float x3, final float y3)
{
final float dx21 = (x2 - x1);
final float dy21 = (y2 - y1);
- ax = 0.0f; ay = 0.0f;
- bx = (x3 - x2) - dx21;
+ ax = 0.0f; // A = 0
+ ay = 0.0f;
+ bx = (x3 - x2) - dx21; // B = P3 - P0 - 2 P2
by = (y3 - y2) - dy21;
- cx = 2.0f * dx21;
+ cx = 2.0f * dx21; // C = 2 (P2 - P1)
cy = 2.0f * dy21;
- dx = x1;
+ dx = x1; // D = P1
dy = y1;
- dax = 0.0f; day = 0.0f;
- dbx = 2.0f * bx; dby = 2.0f * by;
- }
-
- float xat(float t) {
- return t * (t * (t * ax + bx) + cx) + dx;
- }
- float yat(float t) {
- return t * (t * (t * ay + by) + cy) + dy;
- }
-
- float dxat(float t) {
- return t * (t * dax + dbx) + cx;
+ dax = 0.0f;
+ day = 0.0f;
+ dbx = 2.0f * bx;
+ dby = 2.0f * by;
}
- float dyat(float t) {
- return t * (t * day + dby) + cy;
+ void set(final float x1, final float y1,
+ final float x2, final float y2)
+ {
+ final float dx21 = (x2 - x1);
+ final float dy21 = (y2 - y1);
+ ax = 0.0f; // A = 0
+ ay = 0.0f;
+ bx = 0.0f; // B = 0
+ by = 0.0f;
+ cx = dx21; // C = (P2 - P1)
+ cy = dy21;
+ dx = x1; // D = P1
+ dy = y1;
+ dax = 0.0f;
+ day = 0.0f;
+ dbx = 0.0f;
+ dby = 0.0f;
}
- int dxRoots(float[] roots, int off) {
+ int dxRoots(final float[] roots, final int off) {
return Helpers.quadraticRoots(dax, dbx, cx, roots, off);
}
- int dyRoots(float[] roots, int off) {
+ int dyRoots(final float[] roots, final int off) {
return Helpers.quadraticRoots(day, dby, cy, roots, off);
}
- int infPoints(float[] pts, int off) {
+ int infPoints(final float[] pts, final int off) {
// inflection point at t if -f'(t)x*f''(t)y + f'(t)y*f''(t)x == 0
// Fortunately, this turns out to be quadratic, so there are at
// most 2 inflection points.
final float a = dax * dby - dbx * day;
final float b = 2.0f * (cy * dax - day * cx);
final float c = cy * dbx - cx * dby;
return Helpers.quadraticRoots(a, b, c, pts, off);
}
+ int xPoints(final float[] ts, final int off, final float x)
+ {
+ return Helpers.cubicRootsInAB(ax, bx, cx, dx - x, ts, off, 0.0f, 1.0f);
+ }
+
+ int yPoints(final float[] ts, final int off, final float y)
+ {
+ return Helpers.cubicRootsInAB(ay, by, cy, dy - y, ts, off, 0.0f, 1.0f);
+ }
+
// finds points where the first and second derivative are
// perpendicular. This happens when g(t) = f'(t)*f''(t) == 0 (where
// * is a dot product). Unfortunately, we have to solve a cubic.
- private int perpendiculardfddf(float[] pts, int off) {
+ private int perpendiculardfddf(final float[] pts, final int off) {
assert pts.length >= off + 4;
// these are the coefficients of some multiple of g(t) (not g(t),
// because the roots of a polynomial are not changed after multiplication
// by a constant, and this way we save a few multiplications).
- final float a = 2.0f * (dax*dax + day*day);
- final float b = 3.0f * (dax*dbx + day*dby);
- final float c = 2.0f * (dax*cx + day*cy) + dbx*dbx + dby*dby;
- final float d = dbx*cx + dby*cy;
+ final float a = 2.0f * (dax * dax + day * day);
+ final float b = 3.0f * (dax * dbx + day * dby);
+ final float c = 2.0f * (dax * cx + day * cy) + dbx * dbx + dby * dby;
+ final float d = dbx * cx + dby * cy;
+
return Helpers.cubicRootsInAB(a, b, c, d, pts, off, 0.0f, 1.0f);
}
// Tries to find the roots of the function ROC(t)-w in [0, 1). It uses
// a variant of the false position algorithm to find the roots. False
@@ -150,66 +169,69 @@
// first and second derivative are perpendicular, and we pretend these
// are our local extrema. There are at most 3 of these, so we will check
// at most 4 sub-intervals of (0,1). ROC has asymptotes at inflection
// points, so roc-w can have at least 6 roots. This shouldn't be a
// problem for what we're trying to do (draw a nice looking curve).
- int rootsOfROCMinusW(float[] roots, int off, final float w, final float err) {
+ int rootsOfROCMinusW(final float[] roots, final int off, final float w2, final float err) {
// no OOB exception, because by now off<=6, and roots.length >= 10
assert off <= 6 && roots.length >= 10;
+
int ret = off;
- int numPerpdfddf = perpendiculardfddf(roots, off);
- float t0 = 0.0f, ft0 = ROCsq(t0) - w*w;
- roots[off + numPerpdfddf] = 1.0f; // always check interval end points
- numPerpdfddf++;
- for (int i = off; i < off + numPerpdfddf; i++) {
- float t1 = roots[i], ft1 = ROCsq(t1) - w*w;
+ final int end = off + perpendiculardfddf(roots, off);
+ roots[end] = 1.0f; // always check interval end points
+
+ float t0 = 0.0f, ft0 = ROCsq(t0) - w2;
+
+ for (int i = off; i <= end; i++) {
+ float t1 = roots[i], ft1 = ROCsq(t1) - w2;
if (ft0 == 0.0f) {
roots[ret++] = t0;
} else if (ft1 * ft0 < 0.0f) { // have opposite signs
// (ROC(t)^2 == w^2) == (ROC(t) == w) is true because
// ROC(t) >= 0 for all t.
- roots[ret++] = falsePositionROCsqMinusX(t0, t1, w*w, err);
+ roots[ret++] = falsePositionROCsqMinusX(t0, t1, w2, err);
}
t0 = t1;
ft0 = ft1;
}
return ret - off;
}
- private static float eliminateInf(float x) {
+ private static float eliminateInf(final float x) {
return (x == Float.POSITIVE_INFINITY ? Float.MAX_VALUE :
- (x == Float.NEGATIVE_INFINITY ? Float.MIN_VALUE : x));
+ (x == Float.NEGATIVE_INFINITY ? Float.MIN_VALUE : x));
}
// A slight modification of the false position algorithm on wikipedia.
// This only works for the ROCsq-x functions. It might be nice to have
// the function as an argument, but that would be awkward in java6.
// TODO: It is something to consider for java8 (or whenever lambda
// expressions make it into the language), depending on how closures
// and turn out. Same goes for the newton's method
// algorithm in Helpers.java
- private float falsePositionROCsqMinusX(float x0, float x1,
- final float x, final float err)
+ private float falsePositionROCsqMinusX(final float t0, final float t1,
+ final float w2, final float err)
{
final int iterLimit = 100;
int side = 0;
- float t = x1, ft = eliminateInf(ROCsq(t) - x);
- float s = x0, fs = eliminateInf(ROCsq(s) - x);
+ float t = t1, ft = eliminateInf(ROCsq(t) - w2);
+ float s = t0, fs = eliminateInf(ROCsq(s) - w2);
float r = s, fr;
+
for (int i = 0; i < iterLimit && Math.abs(t - s) > err * Math.abs(t + s); i++) {
r = (fs * t - ft * s) / (fs - ft);
- fr = ROCsq(r) - x;
+ fr = ROCsq(r) - w2;
if (sameSign(fr, ft)) {
ft = fr; t = r;
if (side < 0) {
fs /= (1 << (-side));
side--;
} else {
side = -1;
}
- } else if (fr * fs > 0) {
+ } else if (fr * fs > 0.0f) {
fs = fr; s = r;
if (side > 0) {
ft /= (1 << side);
side++;
} else {
@@ -220,24 +242,23 @@
}
}
return r;
}
- private static boolean sameSign(float x, float y) {
+ private static boolean sameSign(final float x, final float y) {
// another way is to test if x*y > 0. This is bad for small x, y.
return (x < 0.0f && y < 0.0f) || (x > 0.0f && y > 0.0f);
}
// returns the radius of curvature squared at t of this curve
// see http://en.wikipedia.org/wiki/Radius_of_curvature_(applications)
private float ROCsq(final float t) {
- // dx=xat(t) and dy=yat(t). These calls have been inlined for efficiency
final float dx = t * (t * dax + dbx) + cx;
final float dy = t * (t * day + dby) + cy;
final float ddx = 2.0f * dax * t + dbx;
final float ddy = 2.0f * day * t + dby;
- final float dx2dy2 = dx*dx + dy*dy;
- final float ddx2ddy2 = ddx*ddx + ddy*ddy;
- final float ddxdxddydy = ddx*dx + ddy*dy;
- return dx2dy2*((dx2dy2*dx2dy2) / (dx2dy2 * ddx2ddy2 - ddxdxddydy*ddxdxddydy));
+ final float dx2dy2 = dx * dx + dy * dy;
+ final float ddx2ddy2 = ddx * ddx + ddy * ddy;
+ final float ddxdxddydy = ddx * dx + ddy * dy;
+ return dx2dy2 * ((dx2dy2 * dx2dy2) / (dx2dy2 * ddx2ddy2 - ddxdxddydy * ddxdxddydy));
}
}
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