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Start implementing new smooth() functions that merge all approaches.

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Work in progress, needs more work on range handling for 'continous', and docs.
This commit is contained in:
Jürg Lehni 2016-01-06 16:11:19 +01:00
parent 2539527864
commit bf4eb47fae
4 changed files with 253 additions and 184 deletions
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13
src/path/CompoundPath.js
View file

@ -135,12 +135,6 @@ var CompoundPath = PathItem.extend(/** @lends CompoundPath# */{
children[i].reverse(); children[i].reverse();
}, },
smooth: function() {
var children = this._children;
for (var i = 0, l = children.length; i < l; i++)
children[i].smooth();
},
// DOCS: reduce() // DOCS: reduce()
// TEST: reduce() // TEST: reduce()
reduce: function reduce(options) { reduce: function reduce(options) {
@ -160,6 +154,13 @@ var CompoundPath = PathItem.extend(/** @lends CompoundPath# */{
return reduce.base.call(this); return reduce.base.call(this);
}, },
// TODO: Docs
smooth: function(options) {
var children = this._children;
for (var i = 0, l = children.length; i < l; i++)
children[i].smooth(options);
},
/** /**
* Specifies whether the compound path is oriented clock-wise. * Specifies whether the compound path is oriented clock-wise.
* *

300
src/path/Path.js
View file

@ -2060,9 +2060,183 @@ var Path = PathItem.extend(/** @lends Path# */{
*/ */
getNearestPoint: function(/* point */) { getNearestPoint: function(/* point */) {
return this.getNearestLocation.apply(this, arguments).getPoint(); return this.getNearestLocation.apply(this, arguments).getPoint();
},
/**
* TODO: continuous:
* Smooths the path by adjusting its curve handles so that the first and
* second derivatives of all involved curves are continuous across their
* boundaries.
*/
/**
* Smooths the path without changing the amount of segments in the path
* or moving their locations, by only smoothing and adjusting the angle and
* length of their handles.
* This works for open paths as well as closed paths.
*
* @param {Object} [options] TODO
* TODO: controls the amount of smoothing as a factor by which to scale each
* handle.
*
* @see Segment#smooth(options)
*
* @example {@paperscript}
* // Smoothing a closed shape:
*
* // Create a rectangular path with its top-left point at
* // {x: 30, y: 25} and a size of {width: 50, height: 50}:
* var path = new Path.Rectangle(new Point(30, 25), new Size(50, 50));
* path.strokeColor = 'black';
*
* // Select the path, so we can see its handles:
* path.fullySelected = true;
*
* // Create a copy of the path and move it 100pt to the right:
* var copy = path.clone();
* copy.position.x += 100;
*
* // Smooth the segments of the copy:
* copy.smooth();
*
* @example {@paperscript height=220}
* var path = new Path();
* path.strokeColor = 'black';
*
* path.add(new Point(30, 50));
*
* var y = 5;
* var x = 3;
*
* for (var i = 0; i < 28; i++) {
* y *= -1.1;
* x *= 1.1;
* path.lineBy(x, y);
* }
*
* // Create a copy of the path and move it 100pt down:
* var copy = path.clone();
* copy.position.y += 120;
*
* // Set its stroke color to red:
* copy.strokeColor = 'red';
*
* // Smooth the segments of the copy:
* copy.smooth();
*/
smooth: function(options) {
function getIndex(value, _default) {
return value == null
? _default
: typeof value === 'number'
? value
: value.getIndex
? value.getIndex()
: _default;
}
var opts = options || {},
type = opts.type,
segments = this._segments,
length = segments.length,
from = getIndex(opts.from, 0),
to = getIndex(opts.to, length - 1);
if (!type || type === 'continuous') {
// Continuous smoothing approach based on work by Lubos Brieda,
// Particle In Cell Consulting LLC, but further simplified by
// addressing handle symmetry across segments, and the possibility
// to process x and y coordinates simultaneously. Also added
// handling of closed paths.
// https://www.particleincell.com/2012/bezier-splines/
var closed = this._closed,
n = length - 1,
// Add overlapping ends for closed paths.
overlap = 0;
if (length <= 2)
return;
if (closed) {
// Overlap by up to 4 points since a current segment is affected
// by 4 neighbors.
overlap = Math.min(length, 4);
n += Math.min(length, overlap) * 2;
}
var knots = [];
for (var i = 0; i < length; i++)
knots[i + overlap] = segments[i]._point;
if (closed) {
// Add the last points again at the beginning, and the first
// ones at the end.
for (var i = 0; i < overlap; i++) {
knots[i] = knots[i + length];
knots[i + length + overlap] = knots[i + overlap];
}
}
// Right-hand side vectors, with left most segment added
var a = [0],
b = [2],
c = [1],
rx = [knots[0]._x + 2 * knots[1]._x],
ry = [knots[0]._y + 2 * knots[1]._y],
n_1 = n - 1;
// Internal segments
for (var i = 1; i < n_1; i++) {
a[i] = 1;
b[i] = 4;
c[i] = 1;
rx[i] = 4 * knots[i]._x + 2 * knots[i + 1]._x;
ry[i] = 4 * knots[i]._y + 2 * knots[i + 1]._y;
}
// Right segment
a[n_1] = 2;
b[n_1] = 7;
c[n_1] = 0;
rx[n_1] = 8 * knots[n_1]._x + knots[n]._x;
ry[n_1] = 8 * knots[n_1]._y + knots[n]._y;
// Solve Ax = b with the Thomas algorithm (from Wikipedia)
for (var i = 1, j = 0; i < n; i++, j++) {
var m = a[i] / b[j];
b[i] = b[i] - m * c[j];
rx[i] = rx[i] - m * rx[j];
ry[i] = ry[i] - m * ry[j];
}
var px = [],
py = [];
px[n_1] = rx[n_1] / b[n_1];
py[n_1] = ry[n_1] / b[n_1];
for (var i = n - 2; i >= 0; i--) {
px[i] = (rx[i] - c[i] * px[i + 1]) / b[i];
py[i] = (ry[i] - c[i] * py[i + 1]) / b[i];
}
px[n] = (3 * knots[n]._x - px[n_1]) / 2;
py[n] = (3 * knots[n]._y - py[n_1]) / 2;
// Now update the segments
n -= overlap;
for (var i = overlap; i <= n; i++) {
var segment = segments[i - overlap],
pt = segment._point,
hx = px[i] - pt._x,
hy = py[i] - pt._y;
if (closed || i < n)
segment.setHandleOut(hx, hy);
if (closed || i > 0)
segment.setHandleIn(-hx, -hy);
}
} else {
// AlL other smoothing methods are handled directly on the segments:
for (var i = from; i <= to; i++)
segments[i].smooth(opts);
}
} }
}), }),
new function() { // Scope for drawing new function() { // Scope for drawing
// Note that in the code below we're often accessing _x and _y on point // Note that in the code below we're often accessing _x and _y on point
// objects that were read from segments. This is because the SegmentPoint // objects that were read from segments. This is because the SegmentPoint
// class overrides the plain x / y properties with getter / setters and // class overrides the plain x / y properties with getter / setters and
@ -2262,132 +2436,6 @@ new function() { // Scope for drawing
} }
}; };
}, },
new function() { // Path Smoothing
/**
* Solves a tri-diagonal system for one of coordinates (x or y) of first
* bezier control points.
*
* @param rhs right hand side vector
* @return Solution vector
*/
function getFirstControlPoints(rhs) {
var n = rhs.length,
x = [], // Solution vector.
tmp = [], // Temporary workspace.
b = 2;
x[0] = rhs[0] / b;
// Decomposition and forward substitution.
for (var i = 1; i < n; i++) {
tmp[i] = 1 / b;
b = (i < n - 1 ? 4 : 2) - tmp[i];
x[i] = (rhs[i] - x[i - 1]) / b;
}
// Back-substitution.
for (var i = 1; i < n; i++) {
x[n - i - 1] -= tmp[n - i] * x[n - i];
}
return x;
}
return {
// NOTE: Documentation for smooth() is in PathItem
smooth: function() {
// This code is based on the work by Oleg V. Polikarpotchkin,
// http://ov-p.spaces.live.com/blog/cns!39D56F0C7A08D703!147.entry
// It was extended to support closed paths by averaging overlapping
// beginnings and ends. The result of this approach is very close to
// Polikarpotchkin's closed curve solution, but reuses the same
// algorithm as for open paths, and is probably executing faster as
// well, so it is preferred.
var segments = this._segments,
size = segments.length,
closed = this._closed,
n = size,
// Add overlapping ends for averaging handles in closed paths
overlap = 0;
if (size <= 2)
return;
if (closed) {
// Overlap up to 4 points since averaging beziers affect the 4
// neighboring points
overlap = Math.min(size, 4);
n += Math.min(size, overlap) * 2;
}
var knots = [];
for (var i = 0; i < size; i++)
knots[i + overlap] = segments[i]._point;
if (closed) {
// If we're averaging, add the 4 last points again at the
// beginning, and the 4 first ones at the end.
for (var i = 0; i < overlap; i++) {
knots[i] = segments[i + size - overlap]._point;
knots[i + size + overlap] = segments[i]._point;
}
} else {
n--;
}
// Calculate first Bezier control points
// Right hand side vector
var rhs = [];
// Set right hand side X values
for (var i = 1; i < n - 1; i++)
rhs[i] = 4 * knots[i]._x + 2 * knots[i + 1]._x;
rhs[0] = knots[0]._x + 2 * knots[1]._x;
rhs[n - 1] = 3 * knots[n - 1]._x;
// Get first control points X-values
var x = getFirstControlPoints(rhs);
// Set right hand side Y values
for (var i = 1; i < n - 1; i++)
rhs[i] = 4 * knots[i]._y + 2 * knots[i + 1]._y;
rhs[0] = knots[0]._y + 2 * knots[1]._y;
rhs[n - 1] = 3 * knots[n - 1]._y;
// Get first control points Y-values
var y = getFirstControlPoints(rhs);
if (closed) {
// Do the actual averaging simply by linearly fading between the
// overlapping values.
for (var i = 0, j = size; i < overlap; i++, j++) {
var f1 = i / overlap,
f2 = 1 - f1,
ie = i + overlap,
je = j + overlap;
// Beginning
x[j] = x[i] * f1 + x[j] * f2;
y[j] = y[i] * f1 + y[j] * f2;
// End
x[je] = x[ie] * f2 + x[je] * f1;
y[je] = y[ie] * f2 + y[je] * f1;
}
n--;
}
var handleIn = null;
// Now set the calculated handles
for (var i = overlap; i <= n - overlap; i++) {
var segment = segments[i - overlap];
if (handleIn)
segment.setHandleIn(handleIn.subtract(segment._point));
if (i < n) {
segment.setHandleOut(
new Point(x[i], y[i]).subtract(segment._point));
handleIn = i < n - 1
? new Point(
2 * knots[i + 1]._x - x[i + 1],
2 * knots[i + 1]._y - y[i + 1])
: new Point(
(knots[n]._x + x[n - 1]) / 2,
(knots[n]._y + y[n - 1]) / 2);
}
}
if (closed && handleIn) {
var segment = this._segments[0];
segment.setHandleIn(handleIn.subtract(segment._point));
}
}
};
},
new function() { // PostScript-style drawing commands new function() { // PostScript-style drawing commands
/** /**
* Helper method that returns the current segment and checks if a moveTo() * Helper method that returns the current segment and checks if a moveTo()

52
src/path/PathItem.js
View file

@ -314,58 +314,6 @@ var PathItem = Item.extend(/** @lends PathItem# */{
/*#*/ } // !__options.nativeContains && __options.booleanOperations /*#*/ } // !__options.nativeContains && __options.booleanOperations
} }
/**
* Smooth bezier curves without changing the amount of segments or their
* points, by only smoothing and adjusting their handle points, for both
* open ended and closed paths.
*
* @name PathItem#smooth
* @function
*
* @example {@paperscript}
* // Smoothing a closed shape:
*
* // Create a rectangular path with its top-left point at
* // {x: 30, y: 25} and a size of {width: 50, height: 50}:
* var path = new Path.Rectangle(new Point(30, 25), new Size(50, 50));
* path.strokeColor = 'black';
*
* // Select the path, so we can see its handles:
* path.fullySelected = true;
*
* // Create a copy of the path and move it 100pt to the right:
* var copy = path.clone();
* copy.position.x += 100;
*
* // Smooth the segments of the copy:
* copy.smooth();
*
* @example {@paperscript height=220}
* var path = new Path();
* path.strokeColor = 'black';
*
* path.add(new Point(30, 50));
*
* var y = 5;
* var x = 3;
*
* for (var i = 0; i < 28; i++) {
* y *= -1.1;
* x *= 1.1;
* path.lineBy(x, y);
* }
*
* // Create a copy of the path and move it 100pt down:
* var copy = path.clone();
* copy.position.y += 120;
*
* // Set its stroke color to red:
* copy.strokeColor = 'red';
*
* // Smooth the segments of the copy:
* copy.smooth();
*/
/** /**
* {@grouptitle Postscript Style Drawing Commands} * {@grouptitle Postscript Style Drawing Commands}
* *

72
src/path/Segment.js
View file

@ -378,6 +378,78 @@ var Segment = Base.extend(/** @lends Segment# */{
|| this._path._closed && segments[0]) || null; || this._path._closed && segments[0]) || null;
}, },
/**
* Smooths the bezier curves that pass through this segment without moving
* its point, by taking into its distance to the neighboring segments and
* changing the direction and length of the segment's handles accordingly.
*
* @param {Object} [options] TODO
* TODO: controls the amount of smoothing as a factor by which to scale each
* handle.
*
* @see PathItem#smooth(options)
*/
smooth: function(options) {
var opts = options || {},
type = opts.type,
factor = opts.factor,
prev = this.getPrevious(),
next = this.getNext(),
// Some precalculations valid for both 'catmull-rom' and 'geometric'
p0 = (prev || this)._point,
p1 = this._point,
p2 = (next || this)._point,
d1 = p0.getDistance(p1),
d2 = p1.getDistance(p2);
if (!type || type === 'catmull-rom') {
// Implementation of by Catmull-Rom splines with factor parameter
// based on work by @nicholaswmin:
// https://github.com/nicholaswmin/VectorTests
// Using these factor values produces different types of splines:
// 0.0: the standard, uniform Catmull-Rom spline
// 0.5: the centripetal Catmull-Rom spline, guaranteeing no self-
// intersections
// 1.0: the chordal Catmull-Rom spline.
var alpha = factor === undefined ? 0.5 : factor,
d1_a = Math.pow(d1, alpha),
d1_2a = d1_a * d1_a,
d2_a = Math.pow(d2, alpha),
d2_2a = d2_a * d2_a;
if (prev) {
var A = 2 * d2_2a + 3 * d2_a * d1_a + d1_2a,
N = 3 * d2_a * (d2_a + d1_a);
this.setHandleIn(N !== 0
? new Point(
(d2_2a * p0._x + A * p1._x - d1_2a * p2._x) / N - p1._x,
(d2_2a * p0._y + A * p1._y - d1_2a * p2._y) / N - p1._y)
: new Point());
}
if (next) {
var A = 2 * d1_2a + 3 * d1_a * d2_a + d2_2a,
N = 3 * d1_a * (d1_a + d2_a);
this.setHandleOut(N !== 0
? new Point(
(d1_2a * p2._x + A * p1._x - d2_2a * p0._x) / N - p1._x,
(d1_2a * p2._y + A * p1._y - d2_2a * p0._y) / N - p1._y)
: new Point());
}
} else if (type === 'geometric') {
// Geometric smoothing approach based on:
// http://www.antigrain.com/research/bezier_interpolation/
// http://scaledinnovation.com/analytics/splines/aboutSplines.html
// http://bseth99.github.io/projects/animate/2-bezier-curves.html
if (prev && next) {
var vector = p0.subtract(p2),
t = factor === undefined ? 0.4 : factor,
k = t * d1 / (d1 + d2);
this.setHandleIn(vector.multiply(k));
this.setHandleOut(vector.multiply(k - t));
}
} else {
throw new Error('Smoothing method \'' + type + '\' not supported.');
}
},
/** /**
* The previous segment in the {@link Path#segments} array that the * The previous segment in the {@link Path#segments} array that the
* segment belongs to. If the segments belongs to a closed path, the last * segment belongs to. If the segments belongs to a closed path, the last