+* +* Here is the copyright notice from ImageMagick: +* +*
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Permission is hereby granted, free of charge, to any person obtaining a %
+% copy of this software and associated documentation files ("ImageMagick"), %
+% to deal in ImageMagick without restriction, including without limitation %
+% the rights to use, copy, modify, merge, publish, distribute, sublicense, %
+% and/or sell copies of ImageMagick, and to permit persons to whom the %
+% ImageMagick is furnished to do so, subject to the following conditions: %
+% %
+% The above copyright notice and this permission notice shall be included in %
+% all copies or substantial portions of ImageMagick. %
+% %
+% The software is provided "as is", without warranty of any kind, express or %
+% implied, including but not limited to the warranties of merchantability, %
+% fitness for a particular purpose and noninfringement. In no event shall %
+% E. I. du Pont de Nemours and Company be liable for any claim, damages or %
+% other liability, whether in an action of contract, tort or otherwise, %
+% arising from, out of or in connection with ImageMagick or the use or other %
+% dealings in ImageMagick. %
+% %
+% Except as contained in this notice, the name of the E. I. du Pont de %
+% Nemours and Company shall not be used in advertising or otherwise to %
+% promote the sale, use or other dealings in ImageMagick without prior %
+% written authorization from the E. I. du Pont de Nemours and Company. %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+*
+*
+* @version 0.90 19 Sep 2000
+* @author Adam Doppelt
+*/
+public class Quantize {
+
+/*
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% %
+% %
+% QQQ U U AAA N N TTTTT IIIII ZZZZZ EEEEE %
+% Q Q U U A A NN N T I ZZ E %
+% Q Q U U AAAAA N N N T I ZZZ EEEEE %
+% Q QQ U U A A N NN T I ZZ E %
+% QQQQ UUU A A N N T IIIII ZZZZZ EEEEE %
+% %
+% %
+% Reduce the Number of Unique Colors in an Image %
+% %
+% %
+% Software Design %
+% John Cristy %
+% July 1992 %
+% %
+% %
+% Copyright 1998 E. I. du Pont de Nemours and Company %
+% %
+% Permission is hereby granted, free of charge, to any person obtaining a %
+% copy of this software and associated documentation files ("ImageMagick"), %
+% to deal in ImageMagick without restriction, including without limitation %
+% the rights to use, copy, modify, merge, publish, distribute, sublicense, %
+% and/or sell copies of ImageMagick, and to permit persons to whom the %
+% ImageMagick is furnished to do so, subject to the following conditions: %
+% %
+% The above copyright notice and this permission notice shall be included in %
+% all copies or substantial portions of ImageMagick. %
+% %
+% The software is provided "as is", without warranty of any kind, express or %
+% implied, including but not limited to the warranties of merchantability, %
+% fitness for a particular purpose and noninfringement. In no event shall %
+% E. I. du Pont de Nemours and Company be liable for any claim, damages or %
+% other liability, whether in an action of contract, tort or otherwise, %
+% arising from, out of or in connection with ImageMagick or the use or other %
+% dealings in ImageMagick. %
+% %
+% Except as contained in this notice, the name of the E. I. du Pont de %
+% Nemours and Company shall not be used in advertising or otherwise to %
+% promote the sale, use or other dealings in ImageMagick without prior %
+% written authorization from the E. I. du Pont de Nemours and Company. %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% Realism in computer graphics typically requires using 24 bits/pixel to
+% generate an image. Yet many graphic display devices do not contain
+% the amount of memory necessary to match the spatial and color
+% resolution of the human eye. The QUANTIZE program takes a 24 bit
+% image and reduces the number of colors so it can be displayed on
+% raster device with less bits per pixel. In most instances, the
+% quantized image closely resembles the original reference image.
+%
+% A reduction of colors in an image is also desirable for image
+% transmission and real-time animation.
+%
+% Function Quantize takes a standard RGB or monochrome images and quantizes
+% them down to some fixed number of colors.
+%
+% For purposes of color allocation, an image is a set of n pixels, where
+% each pixel is a point in RGB space. RGB space is a 3-dimensional
+% vector space, and each pixel, pi, is defined by an ordered triple of
+% red, green, and blue coordinates, (ri, gi, bi).
+%
+% Each primary color component (red, green, or blue) represents an
+% intensity which varies linearly from 0 to a maximum value, cmax, which
+% corresponds to full saturation of that color. Color allocation is
+% defined over a domain consisting of the cube in RGB space with
+% opposite vertices at (0,0,0) and (cmax,cmax,cmax). QUANTIZE requires
+% cmax = 255.
+%
+% The algorithm maps this domain onto a tree in which each node
+% represents a cube within that domain. In the following discussion
+% these cubes are defined by the coordinate of two opposite vertices:
+% The vertex nearest the origin in RGB space and the vertex farthest
+% from the origin.
+%
+% The tree's root node represents the the entire domain, (0,0,0) through
+% (cmax,cmax,cmax). Each lower level in the tree is generated by
+% subdividing one node's cube into eight smaller cubes of equal size.
+% This corresponds to bisecting the parent cube with planes passing
+% through the midpoints of each edge.
+%
+% The basic algorithm operates in three phases: Classification,
+% Reduction, and Assignment. Classification builds a color
+% description tree for the image. Reduction collapses the tree until
+% the number it represents, at most, the number of colors desired in the
+% output image. Assignment defines the output image's color map and
+% sets each pixel's color by reclassification in the reduced tree.
+% Our goal is to minimize the numerical discrepancies between the original
+% colors and quantized colors (quantization error).
+%
+% Classification begins by initializing a color description tree of
+% sufficient depth to represent each possible input color in a leaf.
+% However, it is impractical to generate a fully-formed color
+% description tree in the classification phase for realistic values of
+% cmax. If colors components in the input image are quantized to k-bit
+% precision, so that cmax= 2k-1, the tree would need k levels below the
+% root node to allow representing each possible input color in a leaf.
+% This becomes prohibitive because the tree's total number of nodes is
+% 1 + sum(i=1,k,8k).
+%
+% A complete tree would require 19,173,961 nodes for k = 8, cmax = 255.
+% Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
+% Initializes data structures for nodes only as they are needed; (2)
+% Chooses a maximum depth for the tree as a function of the desired
+% number of colors in the output image (currently log2(colormap size)).
+%
+% For each pixel in the input image, classification scans downward from
+% the root of the color description tree. At each level of the tree it
+% identifies the single node which represents a cube in RGB space
+% containing the pixel's color. It updates the following data for each
+% such node:
+%
+% n1: Number of pixels whose color is contained in the RGB cube
+% which this node represents;
+%
+% n2: Number of pixels whose color is not represented in a node at
+% lower depth in the tree; initially, n2 = 0 for all nodes except
+% leaves of the tree.
+%
+% Sr, Sg, Sb: Sums of the red, green, and blue component values for
+% all pixels not classified at a lower depth. The combination of
+% these sums and n2 will ultimately characterize the mean color of a
+% set of pixels represented by this node.
+%
+% E: The distance squared in RGB space between each pixel contained
+% within a node and the nodes' center. This represents the quantization
+% error for a node.
+%
+% Reduction repeatedly prunes the tree until the number of nodes with
+% n2 > 0 is less than or equal to the maximum number of colors allowed
+% in the output image. On any given iteration over the tree, it selects
+% those nodes whose E count is minimal for pruning and merges their
+% color statistics upward. It uses a pruning threshold, Ep, to govern
+% node selection as follows:
+%
+% Ep = 0
+% while number of nodes with (n2 > 0) > required maximum number of colors
+% prune all nodes such that E <= Ep
+% Set Ep to minimum E in remaining nodes
+%
+% This has the effect of minimizing any quantization error when merging
+% two nodes together.
+%
+% When a node to be pruned has offspring, the pruning procedure invokes
+% itself recursively in order to prune the tree from the leaves upward.
+% n2, Sr, Sg, and Sb in a node being pruned are always added to the
+% corresponding data in that node's parent. This retains the pruned
+% node's color characteristics for later averaging.
+%
+% For each node, n2 pixels exist for which that node represents the
+% smallest volume in RGB space containing those pixel's colors. When n2
+% > 0 the node will uniquely define a color in the output image. At the
+% beginning of reduction, n2 = 0 for all nodes except a the leaves of
+% the tree which represent colors present in the input image.
+%
+% The other pixel count, n1, indicates the total number of colors
+% within the cubic volume which the node represents. This includes n1 -
+% n2 pixels whose colors should be defined by nodes at a lower level in
+% the tree.
+%
+% Assignment generates the output image from the pruned tree. The
+% output image consists of two parts: (1) A color map, which is an
+% array of color descriptions (RGB triples) for each color present in
+% the output image; (2) A pixel array, which represents each pixel as
+% an index into the color map array.
+%
+% First, the assignment phase makes one pass over the pruned color
+% description tree to establish the image's color map. For each node
+% with n2 > 0, it divides Sr, Sg, and Sb by n2 . This produces the
+% mean color of all pixels that classify no lower than this node. Each
+% of these colors becomes an entry in the color map.
+%
+% Finally, the assignment phase reclassifies each pixel in the pruned
+% tree to identify the deepest node containing the pixel's color. The
+% pixel's value in the pixel array becomes the index of this node's mean
+% color in the color map.
+%
+% With the permission of USC Information Sciences Institute, 4676 Admiralty
+% Way, Marina del Rey, California 90292, this code was adapted from module
+% ALCOLS written by Paul Raveling.
+%
+% The names of ISI and USC are not used in advertising or publicity
+% pertaining to distribution of the software without prior specific
+% written permission from ISI.
+%
+*/
+
+final static boolean QUICK = true;
+
+final static int MAX_RGB = 255;
+final static int MAX_NODES = 266817;
+final static int MAX_TREE_DEPTH = 8;
+
+// these are precomputed in advance
+static int SQUARES[];
+static int SHIFT[];
+
+static {
+SQUARES = new int[MAX_RGB + MAX_RGB + 1];
+for (int i= -MAX_RGB; i <= MAX_RGB; i++) {
+ SQUARES[i + MAX_RGB] = i * i;
+}
+
+SHIFT = new int[MAX_TREE_DEPTH + 1];
+for (int i = 0; i < MAX_TREE_DEPTH + 1; ++i) {
+ SHIFT[i] = 1 << (15 - i);
+}
+}
+
+
+/**
+* Reduce the image to the given number of colors. The pixels are
+* reduced in place.
+* @return The new color palette.
+*/
+public static int[] quantizeImage(int pixels[][], int max_colors) {
+Cube cube = new Cube(pixels, max_colors);
+cube.classification();
+cube.reduction();
+cube.assignment();
+return cube.colormap;
+}
+
+static class Cube {
+int pixels[][];
+int max_colors;
+int colormap[];
+
+Node root;
+int depth;
+
+// counter for the number of colors in the cube. this gets
+// recalculated often.
+int colors;
+
+// counter for the number of nodes in the tree
+int nodes;
+
+Cube(int pixels[][], int max_colors) {
+ this.pixels = pixels;
+ this.max_colors = max_colors;
+
+ int i = max_colors;
+ // tree_depth = log max_colors
+ // 4
+ for (depth = 1; i != 0; depth++) {
+ i /= 4;
+ }
+ if (depth > 1) {
+ --depth;
+ }
+ if (depth > MAX_TREE_DEPTH) {
+ depth = MAX_TREE_DEPTH;
+ } else if (depth < 2) {
+ depth = 2;
+ }
+
+ root = new Node(this);
+}
+
+/*
+ * Procedure Classification begins by initializing a color
+ * description tree of sufficient depth to represent each
+ * possible input color in a leaf. However, it is impractical
+ * to generate a fully-formed color description tree in the
+ * classification phase for realistic values of cmax. If
+ * colors components in the input image are quantized to k-bit
+ * precision, so that cmax= 2k-1, the tree would need k levels
+ * below the root node to allow representing each possible
+ * input color in a leaf. This becomes prohibitive because the
+ * tree's total number of nodes is 1 + sum(i=1,k,8k).
+ *
+ * A complete tree would require 19,173,961 nodes for k = 8,
+ * cmax = 255. Therefore, to avoid building a fully populated
+ * tree, QUANTIZE: (1) Initializes data structures for nodes
+ * only as they are needed; (2) Chooses a maximum depth for
+ * the tree as a function of the desired number of colors in
+ * the output image (currently log2(colormap size)).
+ *
+ * For each pixel in the input image, classification scans
+ * downward from the root of the color description tree. At
+ * each level of the tree it identifies the single node which
+ * represents a cube in RGB space containing It updates the
+ * following data for each such node:
+ *
+ * number_pixels : Number of pixels whose color is contained
+ * in the RGB cube which this node represents;
+ *
+ * unique : Number of pixels whose color is not represented
+ * in a node at lower depth in the tree; initially, n2 = 0
+ * for all nodes except leaves of the tree.
+ *
+ * total_red/green/blue : Sums of the red, green, and blue
+ * component values for all pixels not classified at a lower
+ * depth. The combination of these sums and n2 will
+ * ultimately characterize the mean color of a set of pixels
+ * represented by this node.
+ */
+void classification() {
+ int pixels[][] = this.pixels;
+
+ int width = pixels.length;
+ int height = pixels[0].length;
+
+ // convert to indexed color
+ for (int x = width; x-- > 0; ) {
+ for (int y = height; y-- > 0; ) {
+ int pixel = pixels[x][y];
+ int red = (pixel >> 16) & 0xFF;
+ int green = (pixel >> 8) & 0xFF;
+ int blue = (pixel >> 0) & 0xFF;
+
+ // a hard limit on the number of nodes in the tree
+ if (nodes > MAX_NODES) {
+ //System.out.println("pruning");
+ root.pruneLevel();
+ --depth;
+ }
+
+ // walk the tree to depth, increasing the
+ // number_pixels count for each node
+ Node node = root;
+ for (int level = 1; level <= depth; ++level) {
+ int id = (((red > node.mid_red ? 1 : 0) << 0) |
+ ((green > node.mid_green ? 1 : 0) << 1) |
+ ((blue > node.mid_blue ? 1 : 0) << 2));
+ if (node.child[id] == null) {
+ new Node(node, id, level);
+ }
+ node = node.child[id];
+ node.number_pixels += SHIFT[level];
+ }
+
+ ++node.unique;
+ node.total_red += red;
+ node.total_green += green;
+ node.total_blue += blue;
+ }
+ }
+}
+
+/*
+ * reduction repeatedly prunes the tree until the number of
+ * nodes with unique > 0 is less than or equal to the maximum
+ * number of colors allowed in the output image.
+ *
+ * When a node to be pruned has offspring, the pruning
+ * procedure invokes itself recursively in order to prune the
+ * tree from the leaves upward. The statistics of the node
+ * being pruned are always added to the corresponding data in
+ * that node's parent. This retains the pruned node's color
+ * characteristics for later averaging.
+ */
+void reduction() {
+ int threshold = 1;
+ while (colors > max_colors) {
+ colors = 0;
+ threshold = root.reduce(threshold, Integer.MAX_VALUE);
+ }
+}
+
+/**
+ * The result of a closest color search.
+ */
+static class Search {
+ int distance;
+ int color_number;
+}
+
+/*
+ * Procedure assignment generates the output image from the
+ * pruned tree. The output image consists of two parts: (1) A
+ * color map, which is an array of color descriptions (RGB
+ * triples) for each color present in the output image; (2) A
+ * pixel array, which represents each pixel as an index into
+ * the color map array.
+ *
+ * First, the assignment phase makes one pass over the pruned
+ * color description tree to establish the image's color map.
+ * For each node with n2 > 0, it divides Sr, Sg, and Sb by n2.
+ * This produces the mean color of all pixels that classify no
+ * lower than this node. Each of these colors becomes an entry
+ * in the color map.
+ *
+ * Finally, the assignment phase reclassifies each pixel in
+ * the pruned tree to identify the deepest node containing the
+ * pixel's color. The pixel's value in the pixel array becomes
+ * the index of this node's mean color in the color map.
+ */
+void assignment() {
+ colormap = new int[colors];
+
+ colors = 0;
+ root.colormap();
+
+ int pixels[][] = this.pixels;
+
+ int width = pixels.length;
+ int height = pixels[0].length;
+
+ Search search = new Search();
+
+ // convert to indexed color
+ for (int x = width; x-- > 0; ) {
+ for (int y = height; y-- > 0; ) {
+ int pixel = pixels[x][y];
+ int red = (pixel >> 16) & 0xFF;
+ int green = (pixel >> 8) & 0xFF;
+ int blue = (pixel >> 0) & 0xFF;
+
+ // walk the tree to find the cube containing that color
+ Node node = root;
+ for ( ; ; ) {
+ int id = (((red > node.mid_red ? 1 : 0) << 0) |
+ ((green > node.mid_green ? 1 : 0) << 1) |
+ ((blue > node.mid_blue ? 1 : 0) << 2) );
+ if (node.child[id] == null) {
+ break;
+ }
+ node = node.child[id];
+ }
+
+ if (QUICK) {
+ // if QUICK is set, just use that
+ // node. Strictly speaking, this isn't
+ // necessarily best match.
+ pixels[x][y] = node.color_number;
+ } else {
+ // Find the closest color.
+ search.distance = Integer.MAX_VALUE;
+ node.parent.closestColor(red, green, blue, search);
+ pixels[x][y] = search.color_number;
+ }
+ }
+ }
+}
+
+/**
+ * A single Node in the tree.
+ */
+static class Node {
+ Cube cube;
+
+ // parent node
+ Node parent;
+
+ // child nodes
+ Node child[];
+ int nchild;
+
+ // our index within our parent
+ int id;
+ // our level within the tree
+ int level;
+ // our color midpoint
+ int mid_red;
+ int mid_green;
+ int mid_blue;
+
+ // the pixel count for this node and all children
+ int number_pixels;
+
+ // the pixel count for this node
+ int unique;
+ // the sum of all pixels contained in this node
+ int total_red;
+ int total_green;
+ int total_blue;
+
+ // used to build the colormap
+ int color_number;
+
+ Node(Cube cube) {
+ this.cube = cube;
+ this.parent = this;
+ this.child = new Node[8];
+ this.id = 0;
+ this.level = 0;
+
+ this.number_pixels = Integer.MAX_VALUE;
+
+ this.mid_red = (MAX_RGB + 1) >> 1;
+ this.mid_green = (MAX_RGB + 1) >> 1;
+ this.mid_blue = (MAX_RGB + 1) >> 1;
+ }
+
+ Node(Node parent, int id, int level) {
+ this.cube = parent.cube;
+ this.parent = parent;
+ this.child = new Node[8];
+ this.id = id;
+ this.level = level;
+
+ // add to the cube
+ ++cube.nodes;
+ if (level == cube.depth) {
+ ++cube.colors;
+ }
+
+ // add to the parent
+ ++parent.nchild;
+ parent.child[id] = this;
+
+ // figure out our midpoint
+ int bi = (1 << (MAX_TREE_DEPTH - level)) >> 1;
+ mid_red = parent.mid_red + ((id & 1) > 0 ? bi : -bi);
+ mid_green = parent.mid_green + ((id & 2) > 0 ? bi : -bi);
+ mid_blue = parent.mid_blue + ((id & 4) > 0 ? bi : -bi);
+ }
+
+ /**
+ * Remove this child node, and make sure our parent
+ * absorbs our pixel statistics.
+ */
+ void pruneChild() {
+ --parent.nchild;
+ parent.unique += unique;
+ parent.total_red += total_red;
+ parent.total_green += total_green;
+ parent.total_blue += total_blue;
+ parent.child[id] = null;
+ --cube.nodes;
+ cube = null;
+ parent = null;
+ }
+
+ /**
+ * Prune the lowest layer of the tree.
+ */
+ void pruneLevel() {
+ if (nchild != 0) {
+ for (int id = 0; id < 8; id++) {
+ if (child[id] != null) {
+ child[id].pruneLevel();
+ }
+ }
+ }
+ if (level == cube.depth) {
+ pruneChild();
+ }
+ }
+
+ /**
+ * Remove any nodes that have fewer than threshold
+ * pixels. Also, as long as we're walking the tree:
+ *
+ * - figure out the color with the fewest pixels
+ * - recalculate the total number of colors in the tree
+ */
+ int reduce(int threshold, int next_threshold) {
+ if (nchild != 0) {
+ for (int id = 0; id < 8; id++) {
+ if (child[id] != null) {
+ next_threshold = child[id].reduce(threshold, next_threshold);
+ }
+ }
+ }
+ if (number_pixels <= threshold) {
+ pruneChild();
+ } else {
+ if (unique != 0) {
+ cube.colors++;
+ }
+ if (number_pixels < next_threshold) {
+ next_threshold = number_pixels;
+ }
+ }
+ return next_threshold;
+ }
+
+ /*
+ * colormap traverses the color cube tree and notes each
+ * colormap entry. A colormap entry is any node in the
+ * color cube tree where the number of unique colors is
+ * not zero.
+ */
+ void colormap() {
+ if (nchild != 0) {
+ for (int id = 0; id < 8; id++) {
+ if (child[id] != null) {
+ child[id].colormap();
+ }
+ }
+ }
+ if (unique != 0) {
+ int r = ((total_red + (unique >> 1)) / unique);
+ int g = ((total_green + (unique >> 1)) / unique);
+ int b = ((total_blue + (unique >> 1)) / unique);
+ cube.colormap[cube.colors] = ((( 0xFF) << 24) |
+ ((r & 0xFF) << 16) |
+ ((g & 0xFF) << 8) |
+ ((b & 0xFF) << 0));
+ color_number = cube.colors++;
+ }
+ }
+
+ /* ClosestColor traverses the color cube tree at a
+ * particular node and determines which colormap entry
+ * best represents the input color.
+ */
+ void closestColor(int red, int green, int blue, Search search) {
+ if (nchild != 0) {
+ for (int id = 0; id < 8; id++) {
+ if (child[id] != null) {
+ child[id].closestColor(red, green, blue, search);
+ }
+ }
+ }
+
+ if (unique != 0) {
+ int color = cube.colormap[color_number];
+ int distance = distance(color, red, green, blue);
+ if (distance < search.distance) {
+ search.distance = distance;
+ search.color_number = color_number;
+ }
+ }
+ }
+
+ /**
+ * Figure out the distance between this node and som color.
+ */
+ final static int distance(int color, int r, int g, int b) {
+ return (SQUARES[((color >> 16) & 0xFF) - r + MAX_RGB] +
+ SQUARES[((color >> 8) & 0xFF) - g + MAX_RGB] +
+ SQUARES[((color >> 0) & 0xFF) - b + MAX_RGB]);
+ }
+
+ public String toString() {
+ StringBuffer buf = new StringBuffer();
+ if (parent == this) {
+ buf.append("root");
+ } else {
+ buf.append("node");
+ }
+ buf.append(' ');
+ buf.append(level);
+ buf.append(" [");
+ buf.append(mid_red);
+ buf.append(',');
+ buf.append(mid_green);
+ buf.append(',');
+ buf.append(mid_blue);
+ buf.append(']');
+ return new String(buf);
+ }
+}
+}
+}
+
+
+
+
+
diff --git a/src/main/java/jankovicsandras/imagetracer/SVGUtils.java b/src/main/java/jankovicsandras/imagetracer/SVGUtils.java
new file mode 100644
index 0000000..5ef6c30
--- /dev/null
+++ b/src/main/java/jankovicsandras/imagetracer/SVGUtils.java
@@ -0,0 +1,133 @@
+package jankovicsandras.imagetracer;
+
+import java.util.ArrayList;
+import java.util.HashMap;
+import java.util.TreeMap;
+import java.util.Map.Entry;
+
+import jankovicsandras.imagetracer.ImageTracer.IndexedImage;
+
+public class SVGUtils {
+
+
+
+
+ ////////////////////////////////////////////////////////////
+ //
+ // SVG Drawing functions
+ //
+ ////////////////////////////////////////////////////////////
+
+ public static float roundtodec (float val, float places){
+ return (float)(Math.round(val*Math.pow(10,places))/Math.pow(10,places));
+ }
+
+
+ // Getting SVG path element string from a traced path
+ public static void svgpathstring (StringBuilder sb, String desc, ArrayList