4. Create 3D wires and faces
In comparison to sketches which create wires or faces in 2D, the following functions create a wire in 3D. These wires can be used for example to create a 3-dimensional path for a sweep operation. This operation might be needed to create a tube that is bend in a 3-dimensional shape, such as the frame of a chair.
| method | description |
|---|---|
makeLine([point],[point]) |
Create a straight 3D line |
makeCircle(radius,[center],[normal]) |
Create a 3D circle wire |
makeEllipse(major,minor,[center],[normal]) |
Create a 3D ellipse |
makeHelix(pitch,height,radius,[center],[dir],lefthand?) |
Create a 3D helix, center and helix a [x,y,z] |
makeThreePointArc([point1],[point2],[point3]) |
Create 3D arc through 3 points |
makeEllipseArc(major,minor,anglestart,angleEnd,[center],[normal],[xDir?]) |
Create 3D ellipsoid arc |
makeBSplineApproximation([points[],{bezierSplineApproximationConfig}) |
Create a 3D spline approximation through array of points |
{tolerance:1e-3,smoothing:null/[x,y,z],degMax:6,degMin:1} |
bezierSplineApproximationConfig, configuration for spline |
makeBezierCurve([points[]]) |
Create a 3D bezier curve through array of 3D points |
makeTangentArc([startPoint],[tangentPoint],[endPoint]) |
Create a 3D tangent arc, tangentPoint is like vector |
assembleWire([Edges]) ` |
Create a continuous edge from separate wires |
You can not only create wires in 3D but also complete faces. The difference between a wire and a face is that a face consists of a sketch or 3D wire that encloses a surface. This surface can be flat but also bend in space.
| method | description |
|---|---|
makeFace(wire) |
Create a face from a wire consisting only of edges |
makeNewFaceWithinFace(face,wire) |
Create a face on another face using a wire |
makeNonPlanarFace(wire) |
Create a curved surface from a non-planar wire |
makePolygon(points[]) |
Create a face from an array of points in a plane |
makeOffset(face,offset,tolerance) |
Create an offset to a face |
makePlaneFromFace() |
Extend a face out to an infinite plane parallel to this face |
makeSolid(faces[]/shell) |
Create a solid from the volume that is defined by the array of faces or by a surface. |
The following code example demonstrates how faces in 3 dimensions can be created using a quite complicated algorithm. In this example, the faces consisting of triangular surfaces are assembled in such a way that they completely enclose a volume, without leaving a gap. Using the method makeSolid the volume enclosed by these faces can then be converted to a solid. In the image below this is demonstrated by cutting a sphere out of the newly created shape. Note that without this final step, the faces represent infinitely thin surfaces floating in space. This might be sufficient to create a 3D shape for visualization, but does not allow 3D printing the object. The next section will explain the concept of shapes (solids) in more detail.
function projectOnSphere(radius, vertex) {
// function to project a vertex on to a sphere with radius "radius"
let x = vertex[0];
let y = vertex[1];
let z = vertex[2];
let currentRadius = Math.sqrt(
Math.pow(x, 2) + Math.pow(y, 2) + Math.pow(z, 2)
);
let scale = radius / currentRadius;
let scaledVertex = [scale * x, scale * y, scale * z];
return scaledVertex;
}
const icosahedronFaces = (radius) => {
let golden = (1 + Math.sqrt(5)) / 2;
let v = [
// vertices determined by 4 rectangles
projectOnSphere(radius, [-1, golden, 0]),
projectOnSphere(radius, [1, golden, 0]),
projectOnSphere(radius, [-1, -golden, 0]),
projectOnSphere(radius, [1, -golden, 0]),
projectOnSphere(radius, [0, -1, golden]),
projectOnSphere(radius, [0, 1, golden]),
projectOnSphere(radius, [0, -1, -golden]),
projectOnSphere(radius, [0, 1, -golden]),
projectOnSphere(radius, [golden, 0, -1]),
projectOnSphere(radius, [golden, 0, 1]),
projectOnSphere(radius, [-golden, 0, -1]),
projectOnSphere(radius, [-golden, 0, 1]),
];
// faces added so that they always have an edge in common
// with the previous ones
return [
[v[0], v[11], v[5]],
[v[0], v[5], v[1]],
[v[0], v[10], v[11]],
[v[0], v[7], v[10]],
[v[5], v[11], v[4]],
[v[4], v[9], v[5]],
[v[3], v[9], v[4]],
[v[3], v[8], v[9]],
[v[3], v[6], v[8]],
[v[3], v[2], v[6]],
[v[6], v[2], v[10]],
[v[10], v[7], v[6]],
[v[8], v[6], v[7]],
[v[0], v[1], v[7]],
[v[1], v[5], v[9]],
[v[11], v[10], v[2]],
[v[7], v[1], v[8]],
[v[3], v[4], v[2]],
[v[2], v[4], v[11]],
[v[9], v[8], v[1]],
];
};
const main = (
{ makeSolid, sketchRoundedRectangle, makeSphere, makePolygon },
{}
) => {
function makeIcosahedron(radius) {
const faces = icosahedronFaces(radius).map((f) => makePolygon(f));
return makeSolid(faces);
}
// draw the isosphere
let icosahedron = makeIcosahedron(2.0).scale(50);
const sphere = makeSphere(100).translate([90, 30, 20]);
// cut the icosahedron with a sphere to demonstrate that the first
// shape is indeed a solid, no longer collection of faces
icosahedron = icosahedron.cut(sphere)
let shapes = [
{shape: icosahedron, name: "icosehadron", color: "steelblue"}
]
return shapes;
};The following code creates the shape of the OneWorld Trade Center in New York, which is a so-called anti-prism. The shape is created by defining the triangles that make up the shape and then stitching these together to create a solid.
const {draw, drawRectangle, makePolygon, makeSolid} = replicad;
function main()
{
let bL = 200/10; // base length is 200 ft
let h = 1368/10; // height 1368 ft
let m = (60/0.3048)/10; // first 60 meters are straight, converted to feet
function antiPrism(bLength,prismHeight,endScale)
{
let bL = bLength/2;
let tL = bL/Math.sin(Math.PI/4)
let base=[]
base[1] = [-bL,-bL,0];
base[2] = [bL,-bL,0];
base[3] = [bL,bL,0];
base[4] = [-bL,bL,0];
base[5] = base[1] // trick to avoid need for modulus 4
let top=[]
top[1] = [0 ,-tL*endScale ,prismHeight]
top[2] = [tL*endScale , 0 ,prismHeight]
top[3] = [0 ,tL*endScale ,prismHeight]
top[4] = [-tL*endScale ,0 ,prismHeight]
top[5] = top[1] // trick to avoid need for modulus 4
let face=[]
face[1] = makePolygon([base[1],base[4],base[3],base[2]]);
// not defined counterclockwise to have face facing in negative z-direction
for (let i=2 ; i<=8; i+=2)
{
face[i] = makePolygon([top[i/2],base[i/2],base[i/2+1]]);
face[i+1] = makePolygon([base[i/2+1],top[i/2+1],top[i/2]]);
}
face[10] = makePolygon([top[1],top[2],top[3],top[4]]);
return face;
}
let faces = antiPrism(bL,h,Math.sin(Math.PI/4));
let tower = makeSolid(faces).translate(0,0,m);
let towerbase = drawRectangle(bL,bL).sketchOnPlane("XY").extrude(m)
tower = tower.fuse(towerbase)
return tower}