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delaunay.js
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delaunay.js
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import { Vector3 } from "./math.js"
// Delaunay Triangulation from: https://github.com/msavela/delaunay/
class Vertex {
constructor(x, y, z) {
this.x = x
this.y = y
this.z = z
}
equals(vertex) {
return this.x === vertex.x && this.y == vertex.y && this.z == vertex.z
}
}
class Edge {
constructor(v0, v1) {
this.v0 = v0
this.v1 = v1
}
equals(edge) {
return (this.v0.equals(edge.v0) && this.v1.equals(edge.v1)) ||
(this.v0.equals(edge.v1) && this.v1.equals(edge.v0))
}
}
class Triangle {
constructor(v0, v1, v2) {
this.v0 = v0
this.v1 = v1
this.v2 = v2
this.edgeVec0 = new Vector3(v1.x - v0.x, v1.y - v0.y, v1.z - v0.z)
this.edgeVec1 = new Vector3(v2.x - v0.x, v2.y - v0.y, v2.z - v0.z)
this.calcCircumcircle()
}
calcCircumcircle() {
// Reference: http://www.faqs.org/faqs/graphics/algorithms-faq/
// Subject 1.04: How do I generate a circle through three points?
const A = this.v1.x - this.v0.x
const B = this.v1.y - this.v0.y
const C = this.v2.x - this.v0.x
const D = this.v2.y - this.v0.y
const E = A * (this.v0.x + this.v1.x) + B * (this.v0.y + this.v1.y)
const F = C * (this.v0.x + this.v2.x) + D * (this.v0.y + this.v2.y)
const G = 2.0 * (A * (this.v2.y - this.v1.y) - B * (this.v2.x - this.v1.x))
if (G == 0) {
// Collinear points (no circle through them exists) so: get extremes and use midpoint as center.
const minx = Math.min(this.v0.x, this.v1.x, this.v2.x)
const miny = Math.min(this.v0.y, this.v1.y, this.v2.y)
const maxx = Math.max(this.v0.x, this.v1.x, this.v2.x)
const maxy = Math.max(this.v0.y, this.v1.y, this.v2.y)
this.center = new Vertex((minx + maxx) / 2, (miny + maxy) / 2, 0)
const dx = this.center.x - minx
const dy = this.center.y - miny
this.radius = Math.sqrt(dx * dx + dy * dy);
} else {
const cx = (D * E - B * F) / G
const cy = (A * F - C * E) / G
this.center = new Vertex(cx, cy, 0)
const dx = this.center.x - this.v0.x
const dy = this.center.y - this.v0.y
this.radius = Math.sqrt(dx * dx + dy * dy);
}
}
inCircumcircle(v) {
const dx = this.center.x - v.x
const dy = this.center.y - v.y
return Math.sqrt(dx * dx + dy * dy) <= this.radius
}
surfaceNormal() {
return this.edgeVec1.cross(this.edgeVec0)
}
}
function getSuperTriangle(vertices) {
// Initialize with first vertex.
let minX = vertices[0].x
let minY = vertices[0].y
let maxX = vertices[0].x
let maxY = vertices[0].y
// Loop through remaining vertices to find min/max.
for (let i = 1; i < vertices.length; i++) {
const vertex = vertices[i]
minX = Math.min(minX, vertex.x)
minY = Math.min(minY, vertex.y)
maxX = Math.max(maxX, vertex.x)
maxY = Math.max(maxY, vertex.y)
}
const dx = (maxX - minX) * 10
const dy = (maxY - minY) * 10
const v0 = new Vertex(minX - dx, minY - dy * 3, 0)
const v1 = new Vertex(minX - dx, maxY + dy, 0)
const v2 = new Vertex(maxX + dx * 3, maxY + dy, 0)
return new Triangle(v0, v1, v2)
}
function addVertex(vertex, triangles) {
let edges = []
// Remove triangles with circumcircles containing the vertex.
triangles = triangles.filter(triangle => {
if (triangle.inCircumcircle(vertex)) {
edges.push(new Edge(triangle.v0, triangle.v1))
edges.push(new Edge(triangle.v1, triangle.v2))
edges.push(new Edge(triangle.v2, triangle.v0))
return false
}
return true
})
// Get unique edges.
edges = uniqueEdges(edges)
// Create new triangles from the unique edges and new vertex.
edges.forEach(edge => {
triangles.push(new Triangle(edge.v0, edge.v1, vertex))
})
return triangles
}
function uniqueEdges(edges) {
const uniqueEdges = []
for (let i = 0; i < edges.length; ++i) {
let isUnique = true
// See if edge is unique.
for (let j = 0; j < edges.length; ++j) {
if (i != j && edges[i].equals(edges[j])) {
isUnique = false
break
}
}
// Edge is unique, add to unique edges array.
isUnique && uniqueEdges.push(edges[i])
}
return uniqueEdges
}
function bowyerWatson(vertices) {
// Create bounding 'super' triangle.
const st = getSuperTriangle(vertices)
// Initialize triangles while adding bounding triangle.
let triangles = [st]
// Triangulate each vertex.
vertices.forEach(vertex => {
triangles = addVertex(vertex, triangles)
})
// Remove triangles that share edges with super triangle.
triangles = triangles.filter(triangle => {
return !(triangle.v0 == st.v0 || triangle.v0 == st.v1 || triangle.v0 == st.v2 ||
triangle.v1 == st.v0 || triangle.v1 == st.v1 || triangle.v1 == st.v2 ||
triangle.v2 == st.v0 || triangle.v2 == st.v1 || triangle.v2 == st.v2)
})
return triangles
}
export { bowyerWatson, Vertex }