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3D Primitives

‘3D’ stands for three (3) dimensional. A 3D primitive is any shape that has three dimensions, which are often called width, depth, and height (or X, Y, Z.) 3D shapes have a known volume if closed.

The mathematical study of 3D shapes and dimensions is called solid geometry.

Resolution of Shapes

All rounded shapes have a resolution option which controls tesselation. If resolution is set to 8, then 8 polygons are used to create 360 degrees of revolution.

This allows each design to control the amount of detail present, but beware that calculations and rendering time will also increase. For example, the number of polygons increases quadratically with each increase of the resolution for spheres.

EXAMPLE

If the resolution option is omitted, the following resolution is used.

  • CSG.defaultResolution3D = 12

OpenSCAD like functions support the fn parameter, which is the same as resolution.

Cuboid

A three dimensional shape created from six retangular faces, each at right angles to another, and opposite faces are equal. The cube is a special case of the a cuboid in which all six faces are squares.

 Cuboid

Learn about cuboids at MathIsFun.com

Cubes can be created at a requested center. The radius specifies the size of the faces. Cubes with different radius for X, Y and Z axis can be specified by supplying an array of values.

Defaults:

  • size : 1 or [1,1,1]
  • center : [0,0,0]
  • radius : 0
  • round: false
cube({size: 1})
cube({size: [1,2,3]})
cube({size: 1, center: true}) // default center:false
cube({size: 1, center: [false,false,false]}) // individual axis center true or false
cube({size: [1,2,3], round: true})

Also, the CSG library functions can be used directly. NOTE Deprecated in the V2 API

CSG.cube({
    center: [0, 0, 0],
    radius: [1, 1, 1]
})
 
CSG.cube({ // define two opposite corners
    corner1: [4, 4, 4],
    corner2: [5, 4, 2]
})

Rounded cubes are created by specifying a rounded radius for the corners and the sides.

CSG.roundedCube({ // rounded cube
    center: [0, 0, 0],
    radius: 1,
    roundradius: 0.9,
    resolution: 8,
});

Sphere

A three dimensional shape like a ball, where every point on the surface is the same distance from the center.

Sphere

Learn about spheres at MathIsFun.com

Creates a sphere at the requested center. The radius argument determines the size of the sphere. The resolution option determines the number of segments to create in 360 degrees of rotation.

Note: See the start of 3D Primitives for information about the resolution of three dimenional shapes.

Defaults:

  • radius : 1 or [1,1,1]
  • center : [0,0,0]
  • resolution : Resolution3D (12)
sphere(1);
sphere({r: 2});                    // Note: center:true is default (unlike other primitives, as OpenSCAD)
sphere({r: 2, center: true});     // Note: OpenSCAD doesn't support center for sphere but we do
sphere({r: 2, center: [false, false, true]}); // individual axis center 
sphere({r: 10, fn: 100 });
sphere({r: 10, fn: 100, type: 'geodesic'});  // geodesic approach (icosahedron further triangulated)

In case of ``type: 'geodesic'`` the fn tries to match the non-geodesic fn, yet, actually changes in steps of 6 (e.g. fn=6..11 is the same), fn = 1 reveals the base form: the icosahedron.

The CSG library functions can also be used. NOTE Deprecated in the V2 API

CSG.sphere({
  center: [0, 0, 0],
  radius: 2,                      // must be scalar
  resolution: 128
});

Cylinder

A three dimensional shape with two flat ends that are circular or elliptical. The cylinder has the same cross-section from one end to the other.

 Cylinder

Learn about cylinders at MathIsFun.com

The following show examples of creating cylinders. The radius specifies the size about the axis. The resolution option determines the number of segments to create in 360 degrees of rotation.

If necessary then additional options can be provide for start and end points of the axis. As well as start and end radius.

Note: See the start of 3D Primitives for information about the resolution of three dimensional shapes.

Defaults:

  • radius : 1 or
    • radiusStart : 1
    • radiusEnd : 1
  • axis :
    • start : [0,0,-1], end : [0,0,1]
  • resolution : Resolution3D (12)

Note: A start or end radius of 0 creates a cone.

cylinder({r: 1, h: 10})
cylinder({r: 1, h: 10, center: true})   // default: center:false
cylinder({r: 1, h: 10, center: [true, true, false]})
cylinder({r: 1, h: 10, round: true})
cylinder({r1: 3, r2: 0, h: 10})
cylinder({start: [0,0,0], end: [0,0,10], r1: 1, r2: 2, fn: 50})

The CSG library functions can also be used. NOTE: Deprecated in the V2 API

CSG.cylinder({
  start: [0, -1, 0],
  end: [0, 1, 0],
  radius: 1,                        // true cylinder
  resolution: 16
});
 
CSG.cylinder({
  start: [0, -1, 0],
  end: [0, 1, 0],
  radiusStart: 1,                   // start- and end radius defined, partial cones
  radiusEnd: 2,
  resolution: 16
});
 
CSG.roundedCylinder({               // and its rounded version
  start: [0, -1, 0],
  end: [0, 1, 0],
  radius: 1,
  resolution: 16
});

Torus

A three dimensional shape made by revolving a small circle (inner) along the circumference a bigger circle (outer).

 Torus

Learn about torus at MathIsFun.com

A torus is defined as such:

  • Inner Circle
    • ri = inner radius
    • fni = inner resolution
    • roti = inner rotation
  • Outer Circle
    • ro = outer radius
    • fno = outer resolution

Note: See the start of 3D Primitives for information about the resolution of three dimensional shapes.

Defaults:

  • ri : 1
  • fni : 16
  • roti : 0
  • ro : 4
  • fno : 32
torus() 
torus({ ri: 1.5, ro: 3 })
torus({ ri: 0.2 })
 
torus({ fni:4 })           // make inner circle fn = 4 => square
torus({ fni:4,roti:45 })   // rotate inner circle, so flat is top/bottom
torus({ fni:4,fno:4,roti:45 })
torus({ fni:4,fno:5,roti:45 })

Polyhedron

A three dimensional shape where connecting faces create a solid. Each face is a three dimensional polygon (a flat shape with straight sides).

Learn about polyhedrons at MathIsFun.com

Create a polyhedron with a list of points and a list of triangles or polygons. The point list is all the vertexes of the shape, the triangle list is how the points relates to the surfaces of the polyhedron

polyhedron({      // openscad-like (e.g. pyramid)
  points: [ [10,10,0],[10,-10,0],[-10,-10,0],[-10,10,0], // the four points at base
            [0,0,10] ],                                  // the apex point 
  triangles: [ [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
});

Additionally you can also define `polygons: [ [0,1,4,5], [..] ]` too, not just `triangles:`.

You can also create a polyhedron at a more low-level.

var polygons = [];
polygons.push(new CSG.Polygon([
      new CSG.Vertex(new CSG.Vector3D(-5,-5,0)),
      new CSG.Vertex(new CSG.Vector3D(2,2,5)),
      new CSG.Vertex(new CSG.Vector3D(3,3,15))
   ])
);
// add more polygons and finally:
solid = CSG.fromPolygons(polygons);