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133
134
135
136<h1>Geometry Path Strings</h1>
137<p>
138The <b>GoJS</b> <a>Geometry</a> class controls the "shape" of a <a>Shape</a>,
139whereas the <a>Shape.fill</a> and <a>Shape.stroke</a> and other shape properties control the colors and appearance of the shape.
140For common shape figures, there are predefined geometries that can be used by setting <a>Shape.figure</a>.
141However one can also define custom geometries.
142</p>
143<p>
144One can construct any Geometry by allocating and initializing a <a>Geometry</a> of at least one <a>PathFigure</a> holding some <a>PathSegment</a>s.
145But you may find that using the string representation of a Geometry is easier to write and save in a database.
146Use the static method <a>Geometry,parse</a> or the <a>Shape.geometryString</a> property to transform a geometry path string into a <a>Geometry</a> object.
147</p>
148<p>
149See samples that make use of Geometries in the <a href="../samples/index.html#geometries">samples index</a>.
150</p>
151
152<h2 id="GeometryPathStringSyntax">Geometry Path String Syntax</h2>
153<p>
154The syntax for a geometry path string is an extension of the SVG path string syntax.
155The string consists of a number of commands, each a single letter followed by some command-specific numeric parameters.
156</p>
157<p>
158Below are the possible commands along with the parameters they take.
159The parameter notation <code>(x y)+</code> means that the command requires exactly two parameters,
160but there can be 1 or more sets of parameters for each command.
161For instance, the <code>L (x y)+</code> command can be written as <code>L 10 10 20 20</code> to denote two straight line segments.
162</p>
163<p>
164Commands written with an uppercase letter indicate absolute coordinates;
165lowercase commands specify coordinates relative to the last command.
166Some commands do not care about case because they do not take coordinates as arguments.
167</p>
168
169<ul style="padding-left: 0px; list-style: none;">
170<li><pre class="lang-js"><code>M (x y)+</code></pre> Move commands begin a new subpath in a <a>PathFigure</a>.
171One is essential to begin a PathFigure and therefore must be the first segment type in the path string,
172with the exception of a Fill command (<code>F</code>) that can precede it.
173<p>Additional sets of parameters for a move command are automatically considered Line commands,
174so <code>M 10 10 20 20</code> is identical to <code>M 10 10 L 20 20</code>.</li>
175
176<li><pre class="lang-js"><code>L (x y)+</code></pre> Line command adds a straight line segment from the previous point to the new point.</li>
177<li><pre class="lang-js"><code>H (x)+</code></pre> Horizontal line command specifies only an x value for a straight horizontal line.</li>
178<li><pre class="lang-js"><code>V (y)+</code></pre> Vertical line command specifies only a y value for a straight vertical line.</li>
179
180<li><pre class="lang-js"><code>Q (x1 y1 x y)+</code></pre> Quadratic Bezier Curves.
181<code>x1</code>, <code>y1</code> is the control point.
182See <a href="https://www.w3.org/TR/SVG/paths.html#PathDataQuadraticBezierCommands">SVG Quadratic Bezier command</a> for more details.</li>
183<li><pre class="lang-js"><code>T (x y)+</code></pre> Short-hand Quadratic Bezier Curves.
184The control point is calculated based on <a href="https://www.w3.org/TR/SVG/paths.html#PathDataQuadraticBezierCommands">SVG's path rules.</a></li>
185
186<li><pre class="lang-js"><code>C (x1 y1 x2 y2 x y)+</code></pre> Cubic Bezier Curves.
187<code>x1</code>, <code>y1</code> and <code>x2</code>, <code>y2</code> are the control points.
188See <a href="https://www.w3.org/TR/SVG/paths.html#PathDataCubicBezierCommands">SVG Cubic Bezier command</a> for more details.</li>
189<li><pre class="lang-js"><code>S (x2 y2 x y)+</code></pre> Short-hand Cubic Bezier Curves.
190The two control points are calculated based on <a href="https://www.w3.org/TR/SVG/paths.html#PathDataCubicBezierCommands">SVG's path rules.</a></li>
191
192<li><pre class="lang-js"><code>A (rx ry x-axis-rotation large-arc-flag sweep-flag x y)+</code></pre> Elliptical Arcs.
193These follow the <a href="https://www.w3.org/TR/SVG/paths.html#PathDataEllipticalArcCommands">SVG arc conventions</a>.</li>
194
195<li><pre class="lang-js"><code>Z</code></pre> <code>Z</code> denotes that the current segment is closed.
196This is placed after the last segment of a subpath.
197There are no parameters, and case does not matter with this command.</li>
198</ul>
199<hr />
200<p>
201For detailed information on the SVG path strings, see the <a href="https://www.w3.org/TR/SVG/paths.html">W3C's page on SVG Paths</a>.
202<hr />
203
204<p>
205Additionally there are some tokens specific to <b>GoJS</b>:
206<ul style="padding-left: 0px; list-style: none;">
207<li><pre class="lang-js"><code>B (startAngle, sweepAngle, centerX, centerY, radiusX, radiusY) </code></pre> Arcs following <b>GoJS</b> canvas arc convention.
208These arcs create a new line from the last point in the subpath to the first point of an arc defined by the five arguments.
209Unlike all other commands with parameters, multiple sets of parameters are not allowed for B-arcs.
210
211<li><pre class="lang-js"><code>X</code></pre> Used before <code>M</code> commands to denote separate PathFigures instead of a subpath.
212There are no parameters, and case does not matter with this command.
213Separate PathFigures are important when different fills are desired per figure component.</li>
214
215<li><pre class="lang-js"><code>F</code></pre> The existence of this command specifies whether the current PathFigure is filled (true if <code>F</code> is present).
216This is placed at the beginning of a figure.
217There is an optional parameter that is currently ignored.
218Case does not matter with this command.</li>
219
220<li><pre class="lang-js"><code>U</code></pre> The existence of this command specifies whether the current PathFigure is shadowed (<strong>false</strong> if <code>U</code> is present.
221A shadowed PathFigure is the default).
222Shadows on shapes (and therefore PathFigures) only exist if <a>Part.isShadowed</a> is set to true on the containing part.
223This is placed at the beginning of a figure.
224Case does not matter with this command.</li>
225</ul>
226
227<h2 id="GeometryPathStringExamples">Geometry Path String Examples</h2>
228<p>
229Here is a simple usage of a geometry path string when initializing a <a>Shape</a> without setting <a>Shape.figure</a>:
230</p>
231<pre class="lang-js" id="s1"><code>
232diagram.add(
233 $(go.Node,
234 $(go.Shape,
235 { geometryString: "F M120 0 L80 80 0 50z",
236 fill: "lightgreen" })));
237</code></pre>
238<script> goCode("s1", 600, 140)</script>
239<p>
240Here is a geometry path string that uses quadratic Bezier curves:
241</p>
242<pre class="lang-js" id="s2"><code>
243diagram.add(
244 $(go.Node,
245 $(go.Shape,
246 { geometryString: "F M0 0 L100 0 Q150 50 100 100 L0 100 Q50 50 0 0z",
247 fill: "lightgreen" })));
248</code></pre>
249<script> goCode("s2", 600, 140)</script>
250<p>
251This geometry uses <b>GoJS</b> arcs:
252</p>
253<pre class="lang-js" id="s3"><code>
254diagram.add(
255 $(go.Node, "Spot",
256 $(go.Shape,
257 { geometryString: "F M0 0 L80 0 B-90 90 80 20 20 20 L100 100 20 100 B90 90 20 80 20 20z",
258 fill: "lightgreen" }),
259 $(go.TextBlock, "custom shape")
260 ));
261</code></pre>
262<script> goCode("s3", 600, 140)</script>
263<p>
264 The following geometry uses <b>GoJS</b> arcs. Because the <a>Shape</a> is stretched to fit around the <a>TextBlock</a>,
265 and because the default value of <a>Shape.geometryStretch</a> causes the <a>Geometry</a> to be stretched too,
266 the custom geometry is also stretched to fit around the text.
267</p>
268<pre class="lang-js" id="s4"><code>
269diagram.add(
270 $(go.Node, "Auto",
271 $(go.Shape,
272 { geometryString: "F M0 0 L.8 0 B-90 90 .8 .2 .2 .2 L1 1 .2 1 B90 90 .2 .8 .2 .2z",
273 fill: "lightgreen" }),
274 $(go.TextBlock, "custom shape",
275 { margin: 4 })
276 ));
277</code></pre>
278<script>goCode("s4", 600, 140)</script>
279<p>
280In the following Diagram we use a path string that contains three PathFigures.
281Note the <code>X</code> commands separating the figures and the <code>F</code> commands denoting fill.
282</p>
283<pre class="lang-js" id="a"><code>
284diagram.add(
285 $(go.Part,
286 $(go.Shape,
287 { geometryString:
288 "F M 0 0 l 30,30 10,10 35,0 0,-35 x m 50 0 l 0,-50 10,0 35,35 x" +
289 "f m 50 0 l 0,-50 10,0 35,35z",
290 strokeWidth: 10, stroke: "lightblue", fill: "gray" })
291 ));
292</code></pre>
293<script>goCode("a", 600, 140)</script>
294The first two PathFigures are open; the first and third figures are filled.
295The <code>Z</code> command only closes the PathFigure that it ends.
296
297<p>
298In the following Diagram we use a path string that contains four PathFigures, two of which have a shadow.
299Note that figures are shadowed by default if the containing Part has <a>Part.isShadowed</a> set to true.
300To un-shadow specific path figures we use the <code>U</code> command.
301</p>
302<pre class="lang-js" id="a2"><code>
303diagram.add(
304 $(go.Part,
305 { isShadowed: true, shadowOffset: new go.Point(10, 10) },
306 $(go.Shape,
307 { geometryString:
308 "F M 0 0 l 30,30 10,10 35,0 0,-35 x u m 50 0 l 0,-50 10,0 35,35 x" +
309 "u f m 50 0 l 0,-50 10,0 35,35z x m 70 0 l 0,30 30,0 5,-35z",
310 strokeWidth: 8, stroke: "lightblue", fill: "lightcoral" })
311 ));
312</code></pre>
313<script>goCode("a2", 600, 140)</script>
314The first and last PathFigures are shadowed; the second and third are unshadowed.
315
316<h3 id="GeometryParse">Geometry.parse</h3>
317<p>
318Use the static method <a>Geometry,parse</a> to convert a <b>GoJS</b> syntax path string into a <a>Geometry</a>.
319</p>
320<pre class="lang-js" id="s11"><code>
321diagram.add(
322 $(go.Node, "Horizontal",
323 $(go.TextBlock, "Custom Triangle:"),
324 $(go.Shape,
325 { geometry: go.Geometry.parse("M120 0 L80 80 0 50z"), // Geometry is not filled
326 fill: "green", background: "whitesmoke",
327 stroke: "orange", strokeWidth: 2 })
328 ));
329</code></pre>
330<script>goCode("s11", 600, 140)</script>
331<p>
332Note that even though a <a>Shape.fill</a> is specified, the shape does not appear filled.
333This is because the geometry's one <a>PathFigure</a> is not declared to be filled -- there is no <code>F</code> command.
334Importing SVG path strings that are filled also requires declaring that the geometry is filled.
335There are several ways to do that:
336</p>
337<ul>
338 <li>
339 Call <a>Geometry,fillPath</a> for converting the SVG path string to <b>GoJS</b> syntax before calling <a>Geometry,parse</a>.
340 For literal SVG path strings it is often easiest just to prefix it with "F ".
341 </li>
342 <li>Call <a>Geometry,parse</a> with a second argument that is true.</li>
343 <li>Modify the <a>Geometry</a> returned by <a>Geometry,parse</a>, by setting <a>PathFigure.isFilled</a> to true on the desired PathFigures.</li>
344</ul>
345<p>
346Here is the same example, but using a filled geometry path string.
347</p>
348<pre class="lang-js" id="s11a"><code>
349diagram.add(
350 $(go.Node, "Horizontal",
351 $(go.TextBlock, "Custom Triangle:"),
352 $(go.Shape,
353 { geometry: go.Geometry.parse("F M120 0 L80 80 0 50z"), // Geometry is filled
354 fill: "green", background: "whitesmoke",
355 stroke: "orange", strokeWidth: 2 })
356 ));
357</code></pre>
358<script>goCode("s11a", 600, 140)</script>
359
360<p>
361All Geometry objects have bounds that contain the origin,
362so a geometry created with no points at x==0 or y==0 will have extra space to the left of it or above it.
363Note how there is extra space in the following node, causing the shape to appear farther away from the text and shifted down:
364</p>
365<pre class="lang-js" id="s12"><code>
366diagram.add(
367 $(go.Node, "Horizontal",
368 $(go.TextBlock, "Custom Triangle:"),
369 $(go.Shape,
370 { geometry: go.Geometry.parse("M120 50 L80 80 50 50z", true), // Geometry is filled
371 fill: "green", background: "whitesmoke",
372 stroke: "orange", strokeWidth: 2 })
373 ));
374</code></pre>
375<script>goCode("s12", 600, 140)</script>
376<p>
377Often when importing SVG shapes created by drawing applications into <b>GoJS</b> we do not want any extra space above or to the left, so we need to normalize the geometry.
378There is a function for this, <a>Geometry.normalize</a>, which modifies the Geometry's points in-place and returns a Point describing the amount they were offset.
379</p>
380<pre class="lang-js" id="s12a"><code>
381var geo = go.Geometry.parse("M120 50 L80 80 50 50z", true);
382geo.normalize();
383
384diagram.add(
385 $(go.Node, "Horizontal",
386 $(go.TextBlock, "Custom Triangle:"),
387 $(go.Shape,
388 { geometry: geo, // normalized above
389 fill: "green", background: "whitesmoke",
390 stroke: "orange", strokeWidth: 2 })
391 ));
392</code></pre>
393<script>goCode("s12a", 600, 140)</script>
394
395<h3 id="ShapeGeometryString">Shape.geometryString</h3>
396<p>
397The <a>Shape.geometryString</a> property setter parses a given <b>GoJS</b> path string as a Geometry, normalizes it,
398sets the <a>Shape.geometry</a> to this new Geometry, and offsets the Shape's position by the amount it was shifted in normalization.
399The positioning is useful when the shape is inside a <a>Panel,Position</a> panel.
400But when the shape is used in any other kind of panel (thus ignoring the <a>GraphObject.position</a>),
401it is still useful to remove the extra space so that the shape fits in well with the other objects in the panel.
402</p>
403<p>
404The example below adds three Parts with Shapes to the diagram.
405The first shape uses <a>Geometry,parse</a> to set the Shape's Geometry, the second one uses <a>Geometry,parse</a> and <a>Geometry.normalize</a>.
406The third uses <a>Shape.geometryString</a>.
407Note the difference in size between the first Part and the other two.
408</p>
409<pre class="lang-js" id="b"><code>
410var pathstring = "M30 100 C 50 50, 70 20, 100 100, 110, 130, 45, 150, 65, 100";
411
412// Just parsing the geometry
413diagram.add(
414 $(go.Part, "Vertical",
415 $(go.Shape,
416 { geometry: go.Geometry.parse(pathstring),
417 strokeWidth: 10, stroke: "lightcoral",
418 background: "whitesmoke" }),
419 $(go.TextBlock, "parse")
420 ));
421
422// Parsing the geometry and normalizing it
423var geo = go.Geometry.parse(pathstring);
424geo.normalize();
425diagram.add(
426 $(go.Part, "Vertical",
427 $(go.Shape,
428 { geometry: geo,
429 strokeWidth: 10, stroke: "lightgreen",
430 background: "whitesmoke" }),
431 $(go.TextBlock, "parse/normalize")
432 ));
433
434// Using geometryString to parse and normalize the geometry
435diagram.add(
436 $(go.Part, "Vertical",
437 $(go.Shape,
438 { geometryString: pathstring,
439 strokeWidth: 10, stroke: "lightblue",
440 background: "whitesmoke" }),
441 $(go.TextBlock, "geometryString")
442 ));
443
444diagram.layout = $(go.GridLayout);
445
446// Select them all to more easily see their sizes
447diagram.commandHandler.selectAll();
448</code></pre>
449<script>goCode("b", 600, 180)</script>
450
451
452<h2 id="FlippingGeometriesHorizontallyAndVertically">Flipping Geometries Horizontally and Vertically</h2>
453<p>
454 GoJS Geometries have several methods for modifying the geometry's points by a transformation matrix.
455 We can use these methods to flip or mirror the geometries if needed.
456</p>
457<p>
458 <code>geometry.scale(-1, 1)</code> will flip a geometry horizontally.
459 <code>geometry.scale(1, -1)</code> will flip a geometry vertically.
460</p>
461
462<pre class="lang-js" id="b2"><code>
463var pathstring = "M30 100 C 50 50, 70 20, 100 100, 110, 130, 45, 150, 65, 100";
464var geo = go.Geometry.parse(pathstring);
465geo.normalize();
466
467diagram.add(
468$(go.Part, "Vertical",
469 $(go.Shape,
470 { geometry: geo,
471 strokeWidth: 10, stroke: "lightgreen",
472 background: "whitesmoke" }),
473 $(go.TextBlock, "geometry from string\n(normalized)")
474));
475
476var geo2 = geo.copy();
477geo2.scale(-1, 1); // flips a geometry horizontally
478diagram.add(
479$(go.Part, "Vertical",
480 $(go.Shape,
481 { geometry: geo2,
482 strokeWidth: 10, stroke: "lightgreen",
483 background: "whitesmoke" }),
484 $(go.TextBlock, "flipped horizontally")
485));
486
487var geo3 = geo.copy();
488geo3.scale(1, -1); // flips a geometry vertically
489diagram.add(
490$(go.Part, "Vertical",
491 $(go.Shape,
492 { geometry: geo3,
493 strokeWidth: 10, stroke: "lightgreen",
494 background: "whitesmoke" }),
495 $(go.TextBlock, "flipped vertically")
496));
497
498diagram.layout = $(go.GridLayout);
499</code></pre>
500<script>goCode("b2", 600, 180)</script>
501
502<h2 id="ConvertingPathStrings">Converting Path Strings</h2>
503<p>
504The static method <a>Geometry,stringify</a> can be used to output a Geometry as a string.
505This string will have the <b>GoJS</b> path string syntax.
506You can use Geometry.stringify and Geometry.parse to data bind custom shape geometries.
507<p>
508<code>Geometry.parse(Geometry.stringify(myGeometry))</code> will return a geometry equal to <code>myGeometry</code>,
509though if myGeometry was created from a string, the string itself is not guaranteed to be the same.
510If you merely want to copy a Geometry you should use <a>Geometry.copy</a>.
511<p>
512<pre class="lang-js"><code>
513// These path strings represent identical geometries:
514var a = "m0 0 t 50 50, q 40 20, 50 10 h 10 v -23 l 45, 5, 65, 100"
515var b = "M0 0 Q0 0 50 50 Q90 70 100 60 L110 60 L110 37 L155 42 L220 142"
516go.Geometry.stringify(Geometry.parse(a)); // returns the string in b
517go.Geometry.stringify(Geometry.parse(b)); // returns the string in b
518</code></pre>
519
520<p>
521Because of the additional non-SVG commands, a string generated from <a>Geometry,stringify</a> will not necessarily be a valid SVG path.
522</p>
523<p>
524The static method <a>Geometry,fillPath</a> takes a path string of either syntax and adds <code>F</code> tokens before each PathFigure that does not have them.
525Because SVG path strings are not considered to be "filled" by themselves,
526if you are converting an SVG Path shape to <b>GoJS</b> you will want to call <a>Geometry,fillPath</a> on the SVG string.
527</p>
528<pre class="lang-js"><code>
529go.Geometry.fillPath("M0 0 L20 20 L20 0");
530// returns "F M0 0 L20 20 L20 0"
531</code></pre>
532The result can then be passed to <a>Geometry,parse</a> or <a>Shape.geometryString</a>.
533
534<h2 id="ParameterizedGeometries">Parameterized Geometries</h2>
535<p>
536 Although individual <a>Geometry</a> objects cannot be dynamically parameterized based on the intended size or other properties,
537 the <a>Shape</a> class does support such parameterization via <a>Shape,defineFigureGenerator</a>.
538 When you set or bind the <a>Shape.figure</a> property, the shape will call the named figure generator
539 to generate a Geometry appropriate for the desired width and height and other Shape properties.
540</p>
541<p>
542 You can see the definitions of all of the predefined figures in the extensions file:
543 <a href="../extensions/Figures.js" target="_blank">Figures.js</a>.
544</p>
545 </div>
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