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Implemented elliptical arcs for PShapeSVG #2659

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Merged
benfry merged 1 commit into from
Jul 28, 2014
Merged

Implemented elliptical arcs for PShapeSVG #2659

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123 changes: 122 additions & 1 deletion core/src/processing/core/PShapeSVG.java
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Original file line number Diff line number Diff line change
Expand Up @@ -518,7 +518,7 @@ protected void parsePath() {
c == 'S' || c == 's' ||
c == 'Q' || c == 'q' || // quadratic beziers
c == 'T' || c == 't' ||
// c == 'A' || c == 'a' || // elliptical arc
c == 'A' || c == 'a' || // elliptical arc
c == 'Z' || c == 'z' || // closepath
c == ',') {
separate = true;
Expand Down Expand Up @@ -816,6 +816,40 @@ protected void parsePath() {
}
break;

// A - elliptical arc to (absolute)
case 'A': {
float rx = PApplet.parseFloat(pathTokens[i + 1]);
float ry = PApplet.parseFloat(pathTokens[i + 2]);
float angle = PApplet.parseFloat(pathTokens[i + 3]);
boolean fa = PApplet.parseFloat(pathTokens[i + 4]) != 0;
boolean fs = PApplet.parseFloat(pathTokens[i + 5]) != 0;
float endX = PApplet.parseFloat(pathTokens[i + 6]);
float endY = PApplet.parseFloat(pathTokens[i + 7]);
parsePathArcto(cx, cy, rx, ry, angle, fa, fs, endX, endY);
cx = endX;
cy = endY;
i += 8;
prevCurve = true;
}
break;

// a - elliptical arc to (relative)
case 'a': {
float rx = PApplet.parseFloat(pathTokens[i + 1]);
float ry = PApplet.parseFloat(pathTokens[i + 2]);
float angle = PApplet.parseFloat(pathTokens[i + 3]);
boolean fa = PApplet.parseFloat(pathTokens[i + 4]) != 0;
boolean fs = PApplet.parseFloat(pathTokens[i + 5]) != 0;
float endX = cx + PApplet.parseFloat(pathTokens[i + 6]);
float endY = cy + PApplet.parseFloat(pathTokens[i + 7]);
parsePathArcto(cx, cy, rx, ry, angle, fa, fs, endX, endY);
cx = endX;
cy = endY;
i += 8;
prevCurve = true;
}
break;

case 'Z':
case 'z':
// since closing the path, the 'current' point needs
Expand Down Expand Up @@ -924,6 +958,93 @@ private void parsePathQuadto(float cx, float cy,
}


// Approximates elliptical arc by several bezier segments.
// Meets SVG standard requirements from:
// http://www.w3.org/TR/SVG/paths.html#PathDataEllipticalArcCommands
// http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
// Based on arc to bezier curve equations from:
// http://www.spaceroots.org/documents/ellipse/node22.html
private void parsePathArcto(float x1, float y1,
float rx, float ry,
float angle,
boolean fa, boolean fs,
float x2, float y2) {
if (x1 == x2 && y1 == y2) return;
if (rx == 0 || ry == 0) { parsePathLineto(x2, y2); return; }

rx = PApplet.abs(rx); ry = PApplet.abs(ry);

float phi = PApplet.radians(((angle % 360) + 360) % 360);
float cosPhi = PApplet.cos(phi), sinPhi = PApplet.sin(phi);

float x1r = ( cosPhi * (x1 - x2) + sinPhi * (y1 - y2)) / 2;
float y1r = (-sinPhi * (x1 - x2) + cosPhi * (y1 - y2)) / 2;

float cxr, cyr;
{
float A = (x1r*x1r) / (rx*rx) + (y1r*y1r) / (ry*ry);
if (A > 1) {
// No solution, scale ellipse up according to SVG standard
float sqrtA = PApplet.sqrt(A);
rx *= sqrtA; cxr = 0;
ry *= sqrtA; cyr = 0;
} else {
float k = ((fa == fs) ? -1f : 1f) *
PApplet.sqrt((rx*rx * ry*ry) / ((rx*rx * y1r*y1r) + (ry*ry * x1r*x1r)) - 1f);
cxr = k * rx * y1r / ry;
cyr = -k * ry * x1r / rx;
}
}

float cx = cosPhi * cxr - sinPhi * cyr + (x1 + x2) / 2;
float cy = sinPhi * cxr + cosPhi * cyr + (y1 + y2) / 2;

float phi1, phiDelta;
{
float sx = ( x1r - cxr) / rx, sy = ( y1r - cyr) / ry;
float tx = (-x1r - cxr) / rx, ty = (-y1r - cyr) / ry;
phi1 = PApplet.atan2(sy, sx);
phiDelta = (((PApplet.atan2(ty, tx) - phi1) % TWO_PI) + TWO_PI) % TWO_PI;
if (!fs) phiDelta -= TWO_PI;
}

// One segment can not cover more that PI, less than PI/2 is
// recommended to avoid visible inaccuracies caused by rounding errors
int segmentCount = PApplet.ceil(PApplet.abs(phiDelta) / TWO_PI * 4);

float inc = phiDelta / segmentCount;
float a = PApplet.sin(inc) *
(PApplet.sqrt(4 + 3 * PApplet.sq(PApplet.tan(inc / 2))) - 1) / 3;

float sinPhi1 = PApplet.sin(phi1), cosPhi1 = PApplet.cos(phi1);

float p1x = x1;
float p1y = y1;
float relq1x = a * (-rx * cosPhi * sinPhi1 - ry * sinPhi * cosPhi1);
float relq1y = a * (-rx * sinPhi * sinPhi1 + ry * cosPhi * cosPhi1);

for (int i = 0; i < segmentCount; i++) {
float eta = phi1 + (i + 1) * inc;
float sinEta = PApplet.sin(eta), cosEta = PApplet.cos(eta);

float p2x = cx + rx * cosPhi * cosEta - ry * sinPhi * sinEta;
float p2y = cy + rx * sinPhi * cosEta + ry * cosPhi * sinEta;
float relq2x = a * (-rx * cosPhi * sinEta - ry * sinPhi * cosEta);
float relq2y = a * (-rx * sinPhi * sinEta + ry * cosPhi * cosEta);

if (i == segmentCount - 1) { p2x = x2; p2y = y2; }

parsePathCode(BEZIER_VERTEX);
parsePathVertex(p1x + relq1x, p1y + relq1y);
parsePathVertex(p2x - relq2x, p2y - relq2y);
parsePathVertex(p2x, p2y);

p1x = p2x; relq1x = relq2x;
p1y = p2y; relq1y = relq2y;
}
}


/**
* Parse the specified SVG matrix into a PMatrix2D. Note that PMatrix2D
* is rotated relative to the SVG definition, so parameters are rearranged
Expand Down