function main() { var cube = CSG.cube(); return cube; }creates a cube with a radius of 1 and centered at the origin. The code should always contain a main() function. The main() function should return a CSG object (for a 3D solid) or a CAG object (for a 2D area). It's also possible to return multiple objects (a dropdown box will be shown to select the part to be displayed), see rendering multiple objects.

3D solids can be exported as STL files, 2D areas can be exported in a DXF file.

To build your own models, create a .jscad file with your javascript code and parse the file using the OpenJsCad parser. When finished, click on Generate STL and save the result in an .stl file, ready to be printed on your 3d printer.

- Runs in your browser, no need to install any software.
- You can create parametric models with user editable parameters: parameters can be changed in the browser window, without the need to edit the source script. See the Gears demo at the top of this page for example.
- JavaScript is an extremely flexible language, supporting dynamic arrays, object oriented programming, closures, anonymous functions and more
- Solids are stored in variables. This allows for example conditional cloning of objects, something which is nearly impossible in OpenSCAD.
- Properties and Connectors (see below) make it very easy to attach objects to each other at predetermined points, even if you don't know the actual orientation or size.
- Extensive built in support for 2D and 3D math (classes for Vector2D, Vector3D, Plane, Line3D, Line2D)
- Debugging support: step through your code, set breakpoints, inspect variables, etc. See the OpenJsCad parser for details.

- Involute Gears
- Parametric S hook: shows how to extrude 2d paths
- Servo motor: shows how to work with properties and connectors
- Parametric Grille
- Parametric Axis Coupler
- Parametric Lamp Shade: creating 2D panels (for CNC / laser cutting) from a 3D design
- Celtic Knot Ring

- OpenSCAD.jscad: Wrapper functions to ease the translation from OpenSCAD to OpenJsCad, and command line rendering (with node.js) (by René K. Müller)

Contributions are welcome! It's all written in Javascript, so if you know how to use it you know how to modify it as well. To contribute go to OpenJsCad at GitHub (gh-pages tree), create your own fork and send me a pull request. Note that the code is maintained in the gh-pages branch, not the master branch. This is so that it can be accessed directly via Github pages.

`radius: 1`

will give `radius: [1,1,1]`

.
All rounded solids have a 'resolution' parameter which controls tesselation. If resolution is set to 8, then 8 polygons per 360 degree of revolution are used. Beware that rendering time will increase dramatically when increasing the resolution. For a sphere the number of polygons increases quadratically with the resolution used. If the resolution parameter is omitted, the following two global defaults are used: CSG.defaultResolution2D and CSG.defaultResolution3D. The former is used for 2D curves (circle, cylinder), the latter for 3D curves (sphere, 3D expand).

// a cube: var cube = CSG.cube({ center: [0, 0, 0], radius: [1, 1, 1] }); // or alternatively by specifying two diagonally opposite corners: var cube = CSG.cube({ corner1: [-10, 5, 10], corner2: [10, -5, 1] }); // a sphere: var sphere = CSG.sphere({ center: [0, 0, 0], radius: 2, // must be scalar resolution: 32 // optional }); // a cylinder: var cylinder = CSG.cylinder({ start: [0, -1, 0], end: [0, 1, 0], radius: 1, resolution: 16 // optional }); // a cone: var cone = CSG.cylinder({ start: [0, -1, 0], end: [0, 1, 0], radiusStart: 1, radiusEnd: 2, resolution: 16 // optional }); // like a cylinder, but with spherical endpoints: var roundedCylinder = CSG.roundedCylinder({ start: [0, -1, 0], end: [0, 1, 0], radius: 1, resolution: 16 // optional }); // a rounded cube: var cube = CSG.roundedCube({ corner1: [-10, 5, 10], corner2: [10, -5, 1] roundradius: 3, resolution: 8, // optional }); // a polyhedron (point ordering for faces: when looking at the face from the outside inwards, the points must be clockwise): var polyhedron = CSG.polyhedron({ points:[ [10,10,0],[10,-10,0],[-10,-10,0],[-10,10,0], // the four points at base [0,0,10] ], // the apex point faces:[ [0,1,4],[1,2,4],[2,3,4],[3,0,4], // each triangle side [1,0,3],[2,1,3] ] // two triangles for square base });

var csg1 = cube.union(sphere); var csg2 = cube.intersect(sphere); var csg3 = cube.subtract(sphere); // combine multiple solids in one go (faster): var csg1 = cube.union([solid1, solid2, solid3]); var csg2 = cube.intersect([solid1, solid2, solid3]); var csg3 = cube.subtract([solid1, solid2, solid3]);

var cube = CSG.cube(); // translation: var cube2 = cube.translate([1, 2, 3]); // scaling: var largecube = cube.scale(2.0); var stretchedcube = cube.scale([1.5, 1, 0.5]); // rotation: var rotated1 = cube.rotateX(-45); // rotate around the X axis var rotated2 = cube.rotateY(90); // rotate around the Y axis var rotated3 = cube.rotateZ(20); // rotate around the Z axis // combine multiple transforms into a single matrix transform: var m = new CSG.Matrix4x4(); m = m.multiply(CSG.Matrix4x4.rotationX(40)); m = m.multiply(CSG.Matrix4x4.rotationZ(40)); m = m.multiply(CSG.Matrix4x4.translation([-.5, 0, 0])); m = m.multiply(CSG.Matrix4x4.scaling([1.1, 1.2, 1.3])); // and apply the transform: var cube3 = cube.transform(m);

var cube = CSG.cube().translate([1,0,0]); var cube2 = cube.mirroredX(); // mirrored in the x=0 plane var cube3 = cube.mirroredY(); // mirrored in the y=0 plane var cube4 = cube.mirroredZ(); // mirrored in the z=0 plane // create a plane by specifying 3 points: var plane = CSG.Plane.fromPoints([5,0,0], [5, 1, 0], [3, 1, 7]); // and mirror in that plane: var cube5 = cube.mirrored(plane);

var cube = CSG.cube({radius: 10}); // create a plane by specifying 3 points: var plane1 = CSG.Plane.fromPoints([5,0,0], [7, 1, 0], [3, 1, 7]); // or by specifying a normal and a point on the plane: var plane2 = CSG.Plane.fromNormalAndPoint([3, 1, 2], [5, 0, 0]); // and cut by the plane: var part1 = cube.cutByPlane(plane2); // or if we need the other half of the cube: var part2 = cube.cutByPlane(plane2.flipped());

Expansion and contraction are very powerful ways to get an object with nice smooth corners. For example a rounded cube can be created by expanding a normal cube.

Note that these are expensive operations: spheroids are created around every corner and edge in the original object, so the number of polygons quickly increases. Expansion and contraction therefore are only practical for simple non-curved objects.

expand() and contract() take two parameters: the first is the radius of expansion or contraction; the second parameter is optional and specififies the resolution (number of polygons on spherical surfaces, per 360 degree revolution).

var cube1 = CSG.cube({radius: 1.0}); var cube2 = CSG.cube({radius: 1.0}).translate([-0.3, -0.3, -0.3]); var csg = cube1.subtract(cube2); var rounded = csg.expand(0.2, 8);

Properties can have any type, but only the properties of classes supporting a 'transform' method will actually be transformed. This includes CSG.Vector3D, CSG.Plane and CSG.Connector. In particular CSG.Connector properties (see below) can be very useful: these can be used to attach a solid to another solid at a predetermined location regardless of the current orientation.

It's even possible to include a CSG solid as a property of another solid. This could be used for example to define the cutout cylinders to create matching screw holes for an object. Those 'solid properties' get the same transformations as the owning solid but they will not be visible in the result of CSG operations such as union().

Other kind of properties (for example, strings) will still be included in the properties of the transformed solid, but the properties will not get any transformation when the owning solid is transformed.

All primitive solids have some predefined properties, such as the center point of a sphere (TODO: document).

The solid resulting from CSG operations (union(), subtract(), intersect()) will get the merged properties of both source solids. If identically named properties exist, only one of them will be kept.

var cube = CSG.cube({radius: 1.0}); cube.properties.aCorner = new CSG.Vector3D([1, 1, 1]); cube = cube.translate([5, 0, 0]); cube = cube.scale(2); // cube.properties.aCorner will now point to [12, 2, 2], // which is still the same corner point // Properties can be stored in arrays; all properties in the array // will be transformed if the solid is transformed: cube.properties.otherCorners = [ new CSG.Vector3D([-1, 1, 1]), new CSG.Vector3D([-1, -1, 1]) ]; // and we can create sub-property objects; these must be of the // CSG.Properties class. All sub properties will be transformed with // the solid: cube.properties.myProperties = new CSG.Properties(); cube.properties.myProperties.someProperty = new CSG.Vector3D([-1, -1, -1]);For an example see the Servo motor demo.

In other words Connector give us the freedom to rotate and translate objects at will without the need to keep track of their positions and boundaries. And if a third party library exposes connectors for its solids, the user of the library does not have to know the actual dimensions or shapes, only the names of the connector properties.

A CSG.Connector consist of 3 properties:

When connecting two connectors, the solid is transformed such that the

Connectors can be connected by means of two methods:

A CSG solid's

Alternatively we can use a connector's

var cube1 = CSG.cube({radius: 10}); var cube2 = CSG.cube({radius: 4}); // define a connector on the center of one face of cube1 // The connector's axis points outwards and its normal points // towards the positive z axis: cube1.properties.myConnector = new CSG.Connector([10, 0, 0], [1, 0, 0], [0, 0, 1]); // define a similar connector for cube 2: cube2.properties.myConnector = new CSG.Connector([0, -4, 0], [0, -1, 0], [0, 0, 1]); // do some random transformations on cube 1: cube1 = cube1.rotateX(30); cube1 = cube1.translate([3.1, 2, 0]); // Now attach cube2 to cube 1: cube2 = cube2.connectTo( cube2.properties.myConnector, cube1.properties.myConnector, true, // mirror 0 // normalrotation ); // Or alternatively: var matrix = cube2.properties.myConnector.getTransformationTo( cube1.properties.myConnector, true, // mirror 0 // normalrotation ); cube2 = cube2.transform(matrix); var result = cube2.union(cube1);For a more complete example see the Servo motor demo.

lieFlat() lays an object onto the z=0 surface, in such a way that the z-height is minimized and it is centered around the z axis. This can be useful for CNC milling: it will transform a part of an object into the space of the stock material during milling. Or for 3D printing: it is laid in such a way that it can be printed with minimal number of layers. Instead of lieFlat() the function getTransformationToFlatLying() can be used, which returns a CSG.Matrix4x4 for the transformation. Or use getTransformationAndInverseTransformationToFlatLying() to get both the forward transformation and the reverse transformation.

var cube1 = CSG.cube({radius: 10}); var cube2 = CSG.cube({radius: 5}); // get the right bound of cube1 and the left bound of cube2: var deltax = cube1.getBounds()[1].x - cube2.getBounds()[0].x; // align cube2 so it touches cube1: cube2 = cube2.translate([deltax, 0, 0]); var cube3 = CSG.cube({radius: [100,120,10]}); // do some random transformations: cube3 = cube3.rotateZ(31).rotateX(50).translate([30,50,20]); // now place onto the z=0 plane: cube3 = cube3.lieFlat(); // or instead we could have used: var transformation = cube3.getTransformationToFlatLying(); cube3 = cube3.transform(transformation); // or: var obj = cube3.getTransformationAndInverseTransformationToFlatLying(); var forwardtransformation=obj[0]; var backtransformation=obj[1]; cube3 = cube3.transform(forwardtransformation); return cube3;

- union, subtract, intersect
- translate, scale, rotate, mirror. For rotation rotateZ() should be used, which rotates about the origin.
- expand(), contract()

- The extrude() function places the 2D area onto the 3D z=0 plane, and extrudes in the specified direction. Extrusion can be done with an optional twist. This rotates the solid around the z axis (and not necessariy around the extrusion axis) during extrusion. The total degrees of rotation is specified in the twistangle parameter, and twiststeps determine the number of steps between the bottom and top surface.
- To extrude in an arbitrary plane in 3D space, use extrudeInOrthonormalBasis(orthonormalbasis, depth). An orthonormal basis is a combination of a plane and a right-hand vector (read more about orthonormal bases below). depth is the extrusion thickness. This function extrudes symmetrically: half of the extrusion is in front of the plane, half is back from the plane.
- To extrude in one of the standard cartesian planes, use extrudeInPlane(axis1, axis2, depth). axis1 and axis 2 are one of ["X","Y","Z","-X","-Y","-Z"]. The 2D X coordinate is mapped to the 3D axis specified by axis1, and the 2D Y coordinate is mapped to the 3D axis specified by axis2. For example, extrudeInPlane("-Z","X", 10) extrudes such that the 2D x coordinate maps to the 3D negated z coordinate, and the 2D y coordinate maps to the 3D x coordinate.

Note that your main() function may return a CAG object: in this case OpenJsCad will display it as a 'thin' 3D shape. The result can be exported as a DXF file, ready for laser cutting or CNC routing.

// Create a shape; argument is an array of 2D coordinates var shape1 = CAG.fromPoints([[0,0], [5,0], [3,5], [0,5]]); // 2D primitives: var shape2 = CAG.circle({center: [-2, -2], radius: 4, resolution: 20}); var shape3 = CAG.rectangle({center: [5, -2], radius: [2, 3]}); var shape4 = CAG.rectangle({corner1: [-10, 20], corner2: [15, -30]}); var shape5 = CAG.roundedRectangle({center: [5, 7], radius: [4, 4], roundradius: 1, resolution: 24}); var shape6 = CAG.roundedRectangle({corner1: [-2, 3], corner2: [4, -4], roundradius: 1, resolution: 24}); // Expand one of the shapes: first parameter is expand radius, second is the resolution: shape1 = shape1.expand(1, 20); var shape = shape1.union([shape2, shape3, shape4]); // Do some transformations: shape=shape.translate([-2, -2]); shape=shape.rotateZ(20); shape=shape.scale([0.7, 0.9]); // And extrude. This creates a CSG solid: var extruded=shape.extrude({ offset: [0.5, 0, 10], // direction for extrusion twistangle: 30, // top surface is rotated 30 degrees twiststeps: 10 // create 10 slices }); // extrude such that the 2D x coordinate maps to the 3D negated z coordinate, // and the 2D y coordinate maps to the 3D x coordinate: var extruded2=shape.extrudeInPlane("-Z","X", 10); var cube2d = CSG.cube({radius: 10}).rotateZ(45); var z0basis = CSG.OrthoNormalBasis.Z0Plane(); var cag = cube2d.sectionCut(z0basis); // or: var cag = cube2d.projectToOrthoNormalBasis(z0basis);Using a CNC router it's impossible to cut out a true sharp inside corner. The inside corner will be rounded due to the radius of the cutter. The CAG.overCutInsideCorners(radius) function compensates for this by creating an extra cutout at each inner corner so that the actual cut out shape will be at least as large as needed:

var r1=CAG.rectangle({center:[0,0], radius: 4}); var r2=CAG.rectangle({center:[2,0], radius: 2}); var r3=r1.subtract(r2); var cutterradius=1; var r4=r3.overCutInsideCorners(cutterradius); return r4;For an example of 2D shapes see the Parametric S hook demo.

The difference between a 2D Path and a 2D CAG is that a path is a 'thin' line, whereas a CAG is an enclosed area.

Paths can be contructed either by giving a series of 2D coordinates, or through the CSG.Path2D.arc() function, which creates a circular curved path. Paths can be concatenated, the result is a new path.

A path can be converted to a CAG in two ways:

- expandToCAG(pathradius, resolution) traces the path with a circle, in effect making the path's line segments thick.
- innerToCAG() creates a CAG bounded by the path. The path should be a closed path.

var path = new CSG.Path2D([[10,10], [-10,10]], /* closed = */ false); var anotherpath = new CSG.Path2D([[-10,-10]]); path = path.concat(anotherpath); path = path.appendPoint([10,-10]); path = path.close(); // close the path // of course we could simply have done: // var path = new CSG.Path2D([[10,10], [-10,10], [-10,-10], [10,-10]], /* closed = */ true); // We can make arcs and circles. Two methods are provided: // arc() creates an circular segment with a specified center and radius: var curvedpath = CSG.Path2D.arc({ center: [0,0,0], radius: 10, startangle: 0, endangle: 180, resolution: 16, }); // or appendArc() can be used to create a circular or elliptical segment between two endpoints. // appendArc() closely follows the SVG arc specification: // http://www.w3.org/TR/SVG/paths.html#PathDataEllipticalArcCommands // The starting point for the arc is the current endpoint of the path // path2d = path2d.appendArc(endpoint, options); // endpoint is the destination coordinate // options: // .resolution // smoothness of the arc (number of segments per 360 degree of rotation) // to create a circular arc: // .radius // to create an elliptical arc: // .xradius // .yradius // .xaxisrotation // the rotation (in degrees) of the x axis of the ellipse with respect // // to the x axis of our coordinate system // this still leaves 4 possible arcs between the two given points. The following two flags select which one we draw: // .clockwise // = true | false (default is false). Two of the 4 solutions draw clockwise with respect to // // the center point, the other 2 counterclockwise // .large // = true | false (default is false). Two of the 4 solutions are an arc longer than 180 // // degrees, the other two are <= 180 degrees var curvedpath2 = new CSG.Path2D([[0,0], [10,0]]); // create an elliptical arc from [10,0] to [15,0]: curvedpath2 = curvedpath2.appendArc([15,0], { xradius: 4, yradius: -6, xaxisrotation: 30, resolution: 48, clockwise: false, large: true, }); // Extrude the path by following it with a rectangle (upright, perpendicular to the path direction) // Returns a CSG solid // width: width of the extrusion, in the z=0 plane // height: height of the extrusion in the z direction // resolution: number of segments per 360 degrees for the curve in a corner // roundEnds: if true, the ends of the polygon will be rounded, otherwise they will be flat var csg = path.rectangularExtrude(3, 4, 16, true); return csg;

path2d.appendBezier(controlpoints[, options]) - create a single Bézier segment controlpoints: an array of control points. Each control point is a 2d coordinate (can be an [x,y] array or a CSG.Vector2D). The Bézier curve starts at the last point in the existing path2d (hence path2d must not be empty), and ends at the last given control point. Other control points are intermediate control points. The first control point may be null. In that case a smooth transition is ensured: the null control point is replaced by the second last control point of the previous Bézier curve mirrored into the starting point of this curve. In other words the incoming gradient matches the outgoing gradient at the current starting point. options: an optional object. Currently only one option is supported: resolution: controls the smoothness of the curve: at least this number of segments will be used per 360 degree rotation. If omitted, CSG.defaultResolution2D will be used.An example:

var path=new CSG.Path2D([[0,0]]); // beware of the double array: we must pass an array of 2d coordinates // bezier curve from [0,0] to [10,10] // with 3 intermediate control points so it is a 3rd order bezier // Since we do not give a resolution option, CSG.defaultResolution2D is used to determine the number of vertices path = path.appendBezier([[2,8], [5,0], [8,6], [10,10]]); // cubic bezier curve from [10,10] to [10,0] // first control point is null: this forces a smooth transition from the previous bezier curve // In this case the null control point will be replaced by [10,10]+([10,10]-[8,6]) = [12,14] // i.e. the last control point will be mirrored // Here we give the optional options object, setting a resolution of 24 steps per 360 degree of revolution // So the angle between each subsequent side is guaranteed to be less than 15 degrees path = path.appendBezier([null, [10,0]], {resolution: 24}); // close the path and convert to a solid 2D shape: path = path.close(); var cag = path.innerToCAG(); return cag;

To do so, add a function getParameterDefinitions() to your .jscad source. This function should return an array with parameter definitions. Currently 6 parameters types are supported: float, int, text, longtext, bool and choice. The user edited values of the parameters will be supplied as an object parameter to the main() function of your .jscad file.

A float, int, bool or text parameter is created by including the following object in the array returned by getParameterDefinitions():

{ name: 'width', type: 'float', // or 'text', 'int', 'longtext', 'bool' initial: 1.23, // optional, sets the initial value // 'default': 1.23 // this is still supported for backward compatibility but deprecated ('default' is a Javascript keyword) caption: 'Width of the thingy:', // optional, displayed left of the input field // if omitted, the 'name' is displayed (i.e. 'width') }A 'choice' parameter is created using the following object:

{ name: 'shape', type: 'choice', values: ["TRI", "SQU", "CIR"], // these are the values that will be supplied to your script captions: ["Triangle", "Square", "Circle"], // optional, these values are shown in the listbox // if omitted, the items in the 'values' array are used caption: 'Shape:', // optional, displayed left of the input field initial: "SQU", // optional, default selected value // if omitted, the first item is selected by default }To use the values add an argument to your main() function. This argument will be supplied an object with the user edited parameter values:

function main(params) { // custom error checking: if(params.width <= 0) throw new Error("Width should be positive!"); if(params.shape == "TRI") { // do something } }A complete example. Copy/paste it into the Playground at the top of this page to see how it works:

function getParameterDefinitions() { return [ { name: 'width', type: 'float', initial: 10, caption: "Width of the cube:", }, { name: 'height', type: 'float', initial: 14, caption: "Height of the cube:", }, { name: 'depth', type: 'float', initial: 7, caption: "Depth of the cube:", }, { name: 'rounded', type: 'choice', caption: 'Round the corners?', values: [0, 1], captions: ["No thanks", "Yes please"], initial: 1, }, ]; } function main(params) { var result; if(params.rounded == 1) { result = CSG.roundedCube({radius: [params.width, params.height, params.depth], roundradius: 2, resolution: 32}); } else { result = CSG.cube({radius: [params.width, params.height, params.depth]}); } return result; }Or see the Gears demo for another example of interactive parameters.

function main() { var mycube = CSG.cube({radius: 10}); var mycircle = CAG.circle({radius: 10}); // we could just do: // return [mycube, mycircle]; // give each element a description and filename: return [ { name: "cube", // optional, will be used as a prefix for the downloaded stl file caption: "A small cube", // will be shown in the dropdown box data: mycube, }, { name: "circle", // optional, will be used as a prefix for the downloaded dxf file caption: "Circle", data: mycircle, }, ]; }If more than 1 object is returned, a dropdown box is displayed for selecting the part to be displayed and/or downloaded. The jscad is not re-rendered so switching between parts happens fast.

Of course it's still possible to return just a single CSG or CAG:

function main() { return CSG.cube({radius: 10}); }

CSG.OrthoNormalBasis.Z0Plane() creates an orthonormal basis for the z=0 plane. This transforms (xx,yy,zz) 3D coordinates into the 2D (xx, yy) coordinates, or vice versa from (xx, yy) into (xx, yy, 0).

CSG.OrthoNormalBasis.GetCartesian(axis1, axis2) creates an orthonormal basis for the standard XYZ planes. axis1 and axis 2 are one of ["X","Y","Z","-X","-Y","-Z"]. The orthonormal basis is constructed such that the 2D x coordinate is mapped to the 3D axis specified by axis1, and the 2D y coordinate is mapped to the 3D axis specified by axis2.

For example: CSG.OrthoNormalBasis.GetCartesian("-Y","Z") will return an orthonormal basis where the 2D X axis maps to the 3D negated Y axis, and the 2D Y axis maps to the 3D Z axis.

CSG.OrthoNormalBasis.GetCartesian("X","Y") is the same as CSG.OrthoNormalBasis.Z0Plane()

Use to2D() and line3Dto2D() to convert from the 3D space to the 2D plane. Use to3D() and line2Dto3D() to convert the other way.

getProjectionMatrix() gives the projection matrix to transform into the orthonormal basis. getInverseProjectionMatrix() gives the matrix to transform back into the original basis.

// construct a plane: var plane = CSG.Plane.fromNormalAndPoint([1,1,0], [0,0,1]); var orthobasis = new CSG.OrthoNormalBasis(plane); // or if we would like a specific right hand vector: // var orthobasis = new CSG.OrthoNormalBasis(plane, [0,0,1]); var point3d = new CSG.Vector3D(1,5,7); var point2d = orthobasis.to2D(point3d); var projected = orthobasis.to3D(point2d);

function main() { var cube = CSG.cube({radius: 1}); // var volume = cube.getFeatures("volume"); // var area = cube.getFeatures("area"); var features = cube.getFeatures(["volume","area"]); var volume = features[0]; var area = features[1]; OpenJsCad.log("volume: "+volume+"; area: "+area); // volume: 8; area: 24 return cube; }

var cube1 = CSG.cube({radius: 10}); cube1 = cube1.setColor(0.5, 0, 0); var cube2 = CSG.cube({radius: 10}); cube2 = cube2.setColor(0, 0.5, 0); cube2 = cube2.translate([5,1,4]); var result = cube1.subtract(cube2); // the resulting solid will have faces with 2 different colors

// --------- Vector3D --------------------- var vec1 = new CSG.Vector3D(1,2,3); // 3 arguments var vec2 = new CSG.Vector3D( [1,2,3] ); // 1 array argument var vec3 = new CSG.Vector3D(vec2); // cloning a vector // get the values as: vec1.x, vec.y, vec1.z // vector math. All operations return a new vector, the original is unmodified! // vectors cannot be modified. Instead you should create a new vector. vec.negated() vec.abs() vec.plus(othervector) vec.minus(othervector) vec.times(3.0) vec.dividedBy(-5) vec.dot(othervector) vec.lerp(othervector, t) // linear interpolation (0 <= t <= 1) vec.length() vec.lengthSquared() // == vec.length()^2 vec.unit() vec.cross(othervector) // cross product: returns a vector perpendicular to both vec.distanceTo(othervector) vec.distanceToSquared(othervector) // == vec.distanceTo(othervector)^2 vec.equals(othervector) vec.multiply4x4(matrix4x4) // right multiply by a 4x4 matrix vec.min(othervector) // returns a new vector with the minimum x,y and z values vec.max(othervector) // returns a new vector with the maximum x,y and z values // --------- Vector2D --------------------- var vec1 = new CSG.Vector2D(1,2); // 2 arguments var vec2 = new CSG.Vector2D( [1,2] ); // 1 array argument var vec3 = new CSG.Vector2D(vec2); // cloning a vector // vector math. All operations return a new vector, the original is unmodified! vec.negated() vec.abs() vec.plus(othervector) vec.minus(othervector) vec.times(3.0) vec.dividedBy(-5) vec.dot(othervector) vec.lerp(othervector, t) // linear interpolation (0 <= t <= 1) vec.length() vec.lengthSquared() // == vec.length()^2 vec.unit() vec.normal() // returns a 90 degree clockwise rotated vector vec.distanceTo(othervector) vec.distanceToSquared(othervector) // == vec.distanceTo(othervector)^2 vec.cross(othervector) // 2D cross product: returns a scalar vec.equals(othervector) vec.min(othervector) // returns a new vector with the minimum x and y values vec.max(othervector) // returns a new vector with the maximum x and y values vec.multiply4x4(matrix4x4) // right multiply by a 4x4 matrix vec.toVector3D(z) // convert to a vector3D by adding a z coordinate vec.angleDegrees() // returns the angle of the vector: [1,0] = 0 degrees, [0, 1] = 90 degrees, etc vec.angleRadians() // ditto in radians var vec = CSG.Vector2D.fromAngleDegrees(degrees); // returns a vector at the specified angle var vec = CSG.Vector2D.fromAngleRadians(radians); // returns a vector at the specified angle // --------- Matrix4x4 --------------------- var m1 = new CSG.Matrix4x4(); // unity matrix var m2 = new CSG.Matrix4x4( [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1] ); // elements are passed in row order var result = m1.plus(m2); var result = m1.minus(m2); var result = m1.multiply(m2); // matrix vector multiplication (vectors are padded with zeroes to get a 4x1 vector): var vec3d = m1.rightMultiply1x3Vector(vec3d); // matrix * vector var vec3d = m1.leftMultiply1x3Vector(vec3d); // vector * matrix var vec2d = m1.rightMultiply1x2Vector(vec2d); // matrix * vector var vec2d = m1.leftMultiply1x2Vector(vec2d); // vector * matrix // common transformation matrices: var m = CSG.Matrix4x4.rotationX(degrees); // matrix for rotation about X axis var m = CSG.Matrix4x4.rotationY(degrees); // matrix for rotation about Y axis var m = CSG.Matrix4x4.rotationZ(degrees); // matrix for rotation about Z axis var m = CSG.Matrix4x4.rotation(rotationCenter, rotationAxis, degrees); // rotation about arbitrary point and axis var m = CSG.Matrix4x4.translation(vec3d); // translation var m = CSG.Matrix4x4.scaling(vec3d); // scale var m = CSG.Matrix4x4.mirroring(plane); // mirroring in a plane; the argument must be a CSG.Plane // matrix transformations can be concatenated: var transform = CSG.Matrix4x4.rotationX(20).multiply(CSG.Matrix4x4.rotationY(30)); // Use a CSG solid's transform() method to apply the transformation to a CSG solid // ------------ Plane -------------------------- // a 3D plane is represented by a normal vector (should have unit length) and a distance from the origin w // the plane passes through normal.times(w) var plane1 = new CSG.Plane(normal, w); // Or we can construct a plane from 3 points: var plane2 = CSG.Plane.fromPoints(p1, p2, p3); // Or from a normal vector and 1 point: var plane3 = CSG.Plane.fromNormalAndPoint(normal, point); // Flip a plane (front side becomes back side): var plane4 = plane3.flipped(); // Apply transformations (rotation, scaling, translation): var transformed = plane3.transformed(matrix4x4); // argument is a CSG.Matrix4x4 // Intersection of plane and 3d line: var point = plane3.intersectWithLine(line); // argument is CSG.Line3D, returns a CSG.Vector3D // Intersection of 2 planes: var line = plane3.intersectWithPlane(plane); // argument is another CSG.Plane, returns a CSG.Line3D // Distance to point: var w = signedDistanceToPoint(point); // argument is CSG.Vector3D, returns a float (positive // if in front of plane, negative if in back) // ------------ Line3D -------------------------- // A line in 3d space is represented by a point and a direction vector. // Direction should be a unit vector. Point can be any point on the line: var line = new CSG.Line3D(point, direction); // argumenst are CSG.Vector3D // or by giving two points: var line = CSG.Line3D.fromPoints(p1, p2); // argumenst are CSG.Vector3D var point = intersectWithPlane(plane); // == plane.intersectWithLine(this) var line2 = line.reverse(); // same line but reverse direction var line2 = line.transform(matrix4x4); // for rotation, scaling, etc var p = line.closestPointOnLine(point); // project point onto the line var d = line.distanceToPoint(point); // ------------ Line2D -------------------------- // A line in 2d space is represented by a normal vector and a distance w to the // origin along the normal vector // A line in 2d space is represented by a point and a direction vector. // Direction should be a unit vector. Point can be any point on the line: var line = new CSG.Line2D(CSG.Line2D(normal,w)); // or by giving two points: var line = CSG.Line2D.fromPoints(p1, p2); // argumenst are CSG.Vector2D var line2 = line.reverse(); // same line but reverse direction var line2 = line.transform(matrix4x4); // for rotation, scaling, etc var point = line.origin(); // returns the point closest to the origin var dir = line.direction(); // direction vector (CSG.Vector2D) var x = line.xAtY(y); // returns the x coordinate of the line at given y coordinate var d = absDistanceToPoint(point); // returns the absolute distance between a point and the line var p = line.closestPoint(point); // projection of point onto the line var point = line.intersectWithLine(line2); // intersection of two lines, returns CSG.Vector2D