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modules/javafx.graphics/src/main/java/com/sun/marlin/DCurve.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 @@
     double dax, day, dbx, dby;
 
     DCurve() {
     }
 
-    void set(double[] points, int type) {
-        switch(type) {
-        case 8:
+    void set(final double[] 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(double x1, double y1,
-             double x2, double y2,
-             double x3, double y3,
-             double x4, double y4)
+    void set(final double x1, final double y1,
+             final double x2, final double y2,
+             final double x3, final double y3,
+             final double x4, final double y4)
     {
         final double dx32 = 3.0d * (x3 - x2);
         final double dy32 = 3.0d * (y3 - y2);
         final double dx21 = 3.0d * (x2 - x1);
         final double dy21 = 3.0d * (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 = 3.0d * ax; day = 3.0d * ay;
-        dbx = 2.0d * bx; dby = 2.0d * by;
+        dax = 3.0d * ax;
+        day = 3.0d * ay;
+        dbx = 2.0d * bx;
+        dby = 2.0d * by;
     }
 
-    void set(double x1, double y1,
-             double x2, double y2,
-             double x3, double y3)
+    void set(final double x1, final double y1,
+             final double x2, final double y2,
+             final double x3, final double y3)
     {
         final double dx21 = (x2 - x1);
         final double dy21 = (y2 - y1);
-        ax = 0.0d; ay = 0.0d;
-        bx = (x3 - x2) - dx21;
+        ax = 0.0d;              // A = 0
+        ay = 0.0d;
+        bx = (x3 - x2) - dx21;  // B = P3 - P0 - 2 P2
         by = (y3 - y2) - dy21;
-        cx = 2.0d * dx21;
+        cx = 2.0d * dx21;       // C = 2 (P2 - P1)
         cy = 2.0d * dy21;
-        dx = x1;
+        dx = x1;                // D = P1
         dy = y1;
-        dax = 0.0d; day = 0.0d;
-        dbx = 2.0d * bx; dby = 2.0d * by;
-    }
-
-    double xat(double t) {
-        return t * (t * (t * ax + bx) + cx) + dx;
-    }
-    double yat(double t) {
-        return t * (t * (t * ay + by) + cy) + dy;
-    }
-
-    double dxat(double t) {
-        return t * (t * dax + dbx) + cx;
+        dax = 0.0d;
+        day = 0.0d;
+        dbx = 2.0d * bx;
+        dby = 2.0d * by;
     }
 
-    double dyat(double t) {
-        return t * (t * day + dby) + cy;
+    void set(final double x1, final double y1,
+             final double x2, final double y2)
+    {
+        final double dx21 = (x2 - x1);
+        final double dy21 = (y2 - y1);
+        ax = 0.0d;              // A = 0
+        ay = 0.0d;
+        bx = 0.0d;              // B = 0
+        by = 0.0d;
+        cx = dx21;              // C = (P2 - P1)
+        cy = dy21;
+        dx = x1;                // D = P1
+        dy = y1;
+        dax = 0.0d;
+        day = 0.0d;
+        dbx = 0.0d;
+        dby = 0.0d;
     }
 
-    int dxRoots(double[] roots, int off) {
+    int dxRoots(final double[] roots, final int off) {
         return DHelpers.quadraticRoots(dax, dbx, cx, roots, off);
     }
 
-    int dyRoots(double[] roots, int off) {
+    int dyRoots(final double[] roots, final int off) {
         return DHelpers.quadraticRoots(day, dby, cy, roots, off);
     }
 
-    int infPoints(double[] pts, int off) {
+    int infPoints(final double[] 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 double a = dax * dby - dbx * day;
         final double b = 2.0d * (cy * dax - day * cx);
         final double c = cy * dbx - cx * dby;
 
         return DHelpers.quadraticRoots(a, b, c, pts, off);
     }
 
+    int xPoints(final double[] ts, final int off, final double x)
+    {
+        return DHelpers.cubicRootsInAB(ax, bx, cx, dx - x, ts, off, 0.0d, 1.0d);
+    }
+
+    int yPoints(final double[] ts, final int off, final double y)
+    {
+        return DHelpers.cubicRootsInAB(ay, by, cy, dy - y, ts, off, 0.0d, 1.0d);
+    }
+
     // 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(double[] pts, int off) {
+    private int perpendiculardfddf(final double[] 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 double a = 2.0d * (dax*dax + day*day);
-        final double b = 3.0d * (dax*dbx + day*dby);
-        final double c = 2.0d * (dax*cx + day*cy) + dbx*dbx + dby*dby;
-        final double d = dbx*cx + dby*cy;
+        final double a = 2.0d * (dax * dax + day * day);
+        final double b = 3.0d * (dax * dbx + day * dby);
+        final double c = 2.0d * (dax * cx + day * cy) + dbx * dbx + dby * dby;
+        final double d = dbx * cx + dby * cy;
+
         return DHelpers.cubicRootsInAB(a, b, c, d, pts, off, 0.0d, 1.0d);
     }
 
     // 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(double[] roots, int off, final double w, final double err) {
+    int rootsOfROCMinusW(final double[] roots, final int off, final double w2, final double 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);
-        double t0 = 0.0d, ft0 = ROCsq(t0) - w*w;
-        roots[off + numPerpdfddf] = 1.0d; // always check interval end points
-        numPerpdfddf++;
-        for (int i = off; i < off + numPerpdfddf; i++) {
-            double t1 = roots[i], ft1 = ROCsq(t1) - w*w;
+        final int end = off + perpendiculardfddf(roots, off);
+        roots[end] = 1.0d; // always check interval end points
+
+        double t0 = 0.0d, ft0 = ROCsq(t0) - w2;
+
+        for (int i = off; i <= end; i++) {
+            double t1 = roots[i], ft1 = ROCsq(t1) - w2;
             if (ft0 == 0.0d) {
                 roots[ret++] = t0;
             } else if (ft1 * ft0 < 0.0d) { // 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 double eliminateInf(double x) {
+    private static double eliminateInf(final double x) {
         return (x == Double.POSITIVE_INFINITY ? Double.MAX_VALUE :
-            (x == Double.NEGATIVE_INFINITY ? Double.MIN_VALUE : x));
+               (x == Double.NEGATIVE_INFINITY ? Double.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 DHelpers.java
-    private double falsePositionROCsqMinusX(double x0, double x1,
-                                           final double x, final double err)
+    private double falsePositionROCsqMinusX(final double t0, final double t1,
+                                            final double w2, final double err)
     {
         final int iterLimit = 100;
         int side = 0;
-        double t = x1, ft = eliminateInf(ROCsq(t) - x);
-        double s = x0, fs = eliminateInf(ROCsq(s) - x);
+        double t = t1, ft = eliminateInf(ROCsq(t) - w2);
+        double s = t0, fs = eliminateInf(ROCsq(s) - w2);
         double 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 > 0.0d) {
                 fs = fr; s = r;
                 if (side > 0) {
                     ft /= (1 << side);
                     side++;
                 } else {

@@ -220,24 +242,23 @@
             }
         }
         return r;
     }
 
-    private static boolean sameSign(double x, double y) {
+    private static boolean sameSign(final double x, final double y) {
         // another way is to test if x*y > 0. This is bad for small x, y.
         return (x < 0.0d && y < 0.0d) || (x > 0.0d && y > 0.0d);
     }
 
     // returns the radius of curvature squared at t of this curve
     // see http://en.wikipedia.org/wiki/Radius_of_curvature_(applications)
     private double ROCsq(final double t) {
-        // dx=xat(t) and dy=yat(t). These calls have been inlined for efficiency
         final double dx = t * (t * dax + dbx) + cx;
         final double dy = t * (t * day + dby) + cy;
         final double ddx = 2.0d * dax * t + dbx;
         final double ddy = 2.0d * day * t + dby;
-        final double dx2dy2 = dx*dx + dy*dy;
-        final double ddx2ddy2 = ddx*ddx + ddy*ddy;
-        final double ddxdxddydy = ddx*dx + ddy*dy;
-        return dx2dy2*((dx2dy2*dx2dy2) / (dx2dy2 * ddx2ddy2 - ddxdxddydy*ddxdxddydy));
+        final double dx2dy2 = dx * dx + dy * dy;
+        final double ddx2ddy2 = ddx * ddx + ddy * ddy;
+        final double ddxdxddydy = ddx * dx + ddy * dy;
+        return dx2dy2 * ((dx2dy2 * dx2dy2) / (dx2dy2 * ddx2ddy2 - ddxdxddydy * ddxdxddydy));
     }
 }
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