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Fixed Dasher/Renderer float precision + Improved (D)Dasher curve leng…
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…th precision (subdivision) + 4K array tuning + Marlin Settings tuning (larger tiles 128x64, 256x8 subpixels)
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@bourgesl
bourgesl committed Jan 6, 2018
1 parent 8a73533 commit 9cc1757
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Showing 22 changed files with 816 additions and 860 deletions.
2 changes: 1 addition & 1 deletion pom.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@
<groupId>org.marlin</groupId>
<artifactId>marlin</artifactId>
<packaging>jar</packaging>
<version>0.8.2.1-Unsafe</version>
<version>0.9.0-Unsafe</version>
<name>Marlin software rasterizer</name>

<url>https://github.com/bourgesl/marlin-renderer</url>
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77 changes: 32 additions & 45 deletions src/main/java/org/marlin/pisces/Curve.java
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Original file line number Diff line number Diff line change
Expand Up @@ -33,7 +33,7 @@ final class Curve {
Curve() {
}

void set(float[] points, int type) {
void set(final float[] points, final int type) {
switch(type) {
case 8:
set(points[0], points[1],
Expand All @@ -51,10 +51,10 @@ void set(float[] points, int type) {
}
}

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);
Expand All @@ -72,9 +72,9 @@ void set(float x1, float y1,
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);
Expand All @@ -89,30 +89,15 @@ void set(float x1, float y1,
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;
}

float dyat(float t) {
return t * (t * day + dby) + cy;
}

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.
Expand All @@ -126,7 +111,7 @@ int infPoints(float[] pts, int off) {
// 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),
Expand All @@ -152,22 +137,24 @@ private int perpendiculardfddf(float[] pts, int off) {
// 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;
Expand All @@ -176,9 +163,9 @@ int rootsOfROCMinusW(float[] roots, int off, final float w, final float err) {
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.
Expand All @@ -188,17 +175,18 @@ private static float eliminateInf(float x) {
// 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) {
Expand All @@ -207,7 +195,7 @@ private float falsePositionROCsqMinusX(float x0, float x1,
} else {
side = -1;
}
} else if (fr * fs > 0) {
} else if (fr * fs > 0.0f) {
fs = fr; s = r;
if (side > 0) {
ft /= (1 << side);
Expand All @@ -222,15 +210,14 @@ private float falsePositionROCsqMinusX(float x0, float x1,
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;
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77 changes: 32 additions & 45 deletions src/main/java/org/marlin/pisces/DCurve.java
View file
Original file line number Diff line number Diff line change
Expand Up @@ -33,7 +33,7 @@ final class DCurve {
DCurve() {
}

void set(double[] points, int type) {
void set(final double[] points, final int type) {
switch(type) {
case 8:
set(points[0], points[1],
Expand All @@ -51,10 +51,10 @@ void set(double[] points, int type) {
}
}

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);
Expand All @@ -72,9 +72,9 @@ void set(double x1, double y1,
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);
Expand All @@ -89,30 +89,15 @@ void set(double x1, double y1,
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;
}

double dyat(double t) {
return t * (t * day + dby) + cy;
}

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.
Expand All @@ -126,7 +111,7 @@ int infPoints(double[] pts, int off) {
// 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),
Expand All @@ -152,22 +137,24 @@ private int perpendiculardfddf(double[] pts, int off) {
// 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;
Expand All @@ -176,9 +163,9 @@ int rootsOfROCMinusW(double[] roots, int off, final double w, final double err)
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.
Expand All @@ -188,17 +175,18 @@ private static double eliminateInf(double x) {
// 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) {
Expand All @@ -207,7 +195,7 @@ private double falsePositionROCsqMinusX(double x0, double x1,
} else {
side = -1;
}
} else if (fr * fs > 0) {
} else if (fr * fs > 0.0d) {
fs = fr; s = r;
if (side > 0) {
ft /= (1 << side);
Expand All @@ -222,15 +210,14 @@ private double falsePositionROCsqMinusX(double x0, double x1,
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;
Expand Down
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