tldraw/utils/intersections.ts
2021-06-24 13:34:43 +01:00

526 lines
12 KiB
TypeScript

import { Bounds } from 'types'
import vec from 'utils/vec'
import { isAngleBetween } from './utils'
interface Intersection {
didIntersect: boolean
message: string
points: number[][]
}
function getIntersection(message: string, ...points: number[][]) {
return { didIntersect: points.length > 0, message, points }
}
export function intersectRays(
p0: number[],
n0: number[],
p1: number[],
n1: number[]
): Intersection {
const dx = p1[0] - p0[0]
const dy = p1[1] - p0[1]
const det = n1[0] * n0[1] - n1[1] * n0[0]
const u = (dy * n1[0] - dx * n1[1]) / det
const v = (dy * n0[0] - dx * n0[1]) / det
if (u < 0 || v < 0) return getIntersection('miss')
const m0 = n0[1] / n0[0]
const m1 = n1[1] / n1[0]
const b0 = p0[1] - m0 * p0[0]
const b1 = p1[1] - m1 * p1[0]
const x = (b1 - b0) / (m0 - m1)
const y = m0 * x + b0
return Number.isFinite(x)
? getIntersection('intersection', [x, y])
: getIntersection('parallel')
}
export function intersectLineSegments(
a1: number[],
a2: number[],
b1: number[],
b2: number[]
): Intersection {
const AB = vec.sub(a1, b1)
const BV = vec.sub(b2, b1)
const AV = vec.sub(a2, a1)
const ua_t = BV[0] * AB[1] - BV[1] * AB[0]
const ub_t = AV[0] * AB[1] - AV[1] * AB[0]
const u_b = BV[1] * AV[0] - BV[0] * AV[1]
if (ua_t === 0 || ub_t === 0) {
return getIntersection('coincident')
}
if (u_b === 0) {
return getIntersection('parallel')
}
if (u_b != 0) {
const ua = ua_t / u_b
const ub = ub_t / u_b
if (0 <= ua && ua <= 1 && 0 <= ub && ub <= 1) {
return getIntersection('intersection', vec.add(a1, vec.mul(AV, ua)))
}
}
return getIntersection('no intersection')
}
export function intersectCircleCircle(a: number[], b: number[]): Intersection {
const R = a[2],
r = b[2]
let dx = b[0] - a[0],
dy = b[1] - a[1]
const d = Math.sqrt(dx * dx + dy * dy),
x = (d * d - r * r + R * R) / (2 * d),
y = Math.sqrt(R * R - x * x)
dx /= d
dy /= d
return getIntersection(
'intersection',
[a[0] + dx * x - dy * y, a[1] + dy * x + dx * y],
[a[0] + dx * x + dy * y, a[1] + dy * x - dx * y]
)
}
export function intersectCircleLineSegment(
c: number[],
r: number,
a1: number[],
a2: number[]
): Intersection {
const a =
(a2[0] - a1[0]) * (a2[0] - a1[0]) + (a2[1] - a1[1]) * (a2[1] - a1[1])
const b =
2 * ((a2[0] - a1[0]) * (a1[0] - c[0]) + (a2[1] - a1[1]) * (a1[1] - c[1]))
const cc =
c[0] * c[0] +
c[1] * c[1] +
a1[0] * a1[0] +
a1[1] * a1[1] -
2 * (c[0] * a1[0] + c[1] * a1[1]) -
r * r
const deter = b * b - 4 * a * cc
if (deter < 0) {
return getIntersection('outside')
}
if (deter === 0) {
return getIntersection('tangent')
}
const e = Math.sqrt(deter)
const u1 = (-b + e) / (2 * a)
const u2 = (-b - e) / (2 * a)
if ((u1 < 0 || u1 > 1) && (u2 < 0 || u2 > 1)) {
if ((u1 < 0 && u2 < 0) || (u1 > 1 && u2 > 1)) {
return getIntersection('outside')
} else {
return getIntersection('inside')
}
}
const results: number[][] = []
if (0 <= u1 && u1 <= 1) results.push(vec.lrp(a1, a2, u1))
if (0 <= u2 && u2 <= 1) results.push(vec.lrp(a1, a2, u2))
return getIntersection('intersection', ...results)
}
export function intersectEllipseLineSegment(
center: number[],
rx: number,
ry: number,
a1: number[],
a2: number[],
rotation = 0
): Intersection {
// If the ellipse or line segment are empty, return no tValues.
if (rx === 0 || ry === 0 || vec.isEqual(a1, a2)) {
return getIntersection('No intersection')
}
// Get the semimajor and semiminor axes.
rx = rx < 0 ? rx : -rx
ry = ry < 0 ? ry : -ry
// Rotate points and translate so the ellipse is centered at the origin.
a1 = vec.sub(vec.rotWith(a1, center, -rotation), center)
a2 = vec.sub(vec.rotWith(a2, center, -rotation), center)
// Calculate the quadratic parameters.
const diff = vec.sub(a2, a1)
const A = (diff[0] * diff[0]) / rx / rx + (diff[1] * diff[1]) / ry / ry
const B = (2 * a1[0] * diff[0]) / rx / rx + (2 * a1[1] * diff[1]) / ry / ry
const C = (a1[0] * a1[0]) / rx / rx + (a1[1] * a1[1]) / ry / ry - 1
// Make a list of t values (normalized points on the line where intersections occur).
const tValues: number[] = []
// Calculate the discriminant.
const discriminant = B * B - 4 * A * C
if (discriminant === 0) {
// One real solution.
tValues.push(-B / 2 / A)
} else if (discriminant > 0) {
const root = Math.sqrt(discriminant)
// Two real solutions.
tValues.push((-B + root) / 2 / A)
tValues.push((-B - root) / 2 / A)
}
// Filter to only points that are on the segment.
// Solve for points, then counter-rotate points.
const points = tValues
.filter((t) => t >= 0 && t <= 1)
.map((t) => vec.add(center, vec.add(a1, vec.mul(vec.sub(a2, a1), t))))
.map((p) => vec.rotWith(p, center, rotation))
return getIntersection('intersection', ...points)
}
export function intersectArcLineSegment(
start: number[],
end: number[],
center: number[],
radius: number,
A: number[],
B: number[]
): Intersection {
const sa = vec.angle(center, start)
const ea = vec.angle(center, end)
const ellipseTest = intersectEllipseLineSegment(center, radius, radius, A, B)
if (!ellipseTest.didIntersect) return getIntersection('No intersection')
const points = ellipseTest.points.filter((point) =>
isAngleBetween(sa, ea, vec.angle(center, point))
)
if (points.length === 0) {
return getIntersection('No intersection')
}
return getIntersection('intersection', ...points)
}
export function intersectCircleRectangle(
c: number[],
r: number,
point: number[],
size: number[]
): Intersection[] {
const tl = point
const tr = vec.add(point, [size[0], 0])
const br = vec.add(point, size)
const bl = vec.add(point, [0, size[1]])
const intersections: Intersection[] = []
const topIntersection = intersectCircleLineSegment(c, r, tl, tr)
const rightIntersection = intersectCircleLineSegment(c, r, tr, br)
const bottomIntersection = intersectCircleLineSegment(c, r, bl, br)
const leftIntersection = intersectCircleLineSegment(c, r, tl, bl)
if (topIntersection.didIntersect) {
intersections.push({ ...topIntersection, message: 'top' })
}
if (rightIntersection.didIntersect) {
intersections.push({ ...rightIntersection, message: 'right' })
}
if (bottomIntersection.didIntersect) {
intersections.push({ ...bottomIntersection, message: 'bottom' })
}
if (leftIntersection.didIntersect) {
intersections.push({ ...leftIntersection, message: 'left' })
}
return intersections
}
export function intersectEllipseRectangle(
c: number[],
rx: number,
ry: number,
point: number[],
size: number[],
rotation = 0
): Intersection[] {
const tl = point
const tr = vec.add(point, [size[0], 0])
const br = vec.add(point, size)
const bl = vec.add(point, [0, size[1]])
const intersections: Intersection[] = []
const topIntersection = intersectEllipseLineSegment(
c,
rx,
ry,
tl,
tr,
rotation
)
const rightIntersection = intersectEllipseLineSegment(
c,
rx,
ry,
tr,
br,
rotation
)
const bottomIntersection = intersectEllipseLineSegment(
c,
rx,
ry,
bl,
br,
rotation
)
const leftIntersection = intersectEllipseLineSegment(
c,
rx,
ry,
tl,
bl,
rotation
)
if (topIntersection.didIntersect) {
intersections.push({ ...topIntersection, message: 'top' })
}
if (rightIntersection.didIntersect) {
intersections.push({ ...rightIntersection, message: 'right' })
}
if (bottomIntersection.didIntersect) {
intersections.push({ ...bottomIntersection, message: 'bottom' })
}
if (leftIntersection.didIntersect) {
intersections.push({ ...leftIntersection, message: 'left' })
}
return intersections
}
export function intersectRectangleLineSegment(
point: number[],
size: number[],
a1: number[],
a2: number[]
): Intersection[] {
const tl = point
const tr = vec.add(point, [size[0], 0])
const br = vec.add(point, size)
const bl = vec.add(point, [0, size[1]])
const intersections: Intersection[] = []
const topIntersection = intersectLineSegments(a1, a2, tl, tr)
const rightIntersection = intersectLineSegments(a1, a2, tr, br)
const bottomIntersection = intersectLineSegments(a1, a2, bl, br)
const leftIntersection = intersectLineSegments(a1, a2, tl, bl)
if (topIntersection.didIntersect) {
intersections.push({ ...topIntersection, message: 'top' })
}
if (rightIntersection.didIntersect) {
intersections.push({ ...rightIntersection, message: 'right' })
}
if (bottomIntersection.didIntersect) {
intersections.push({ ...bottomIntersection, message: 'bottom' })
}
if (leftIntersection.didIntersect) {
intersections.push({ ...leftIntersection, message: 'left' })
}
return intersections
}
export function intersectArcRectangle(
start: number[],
end: number[],
center: number[],
radius: number,
point: number[],
size: number[]
): Intersection[] {
const tl = point
const tr = vec.add(point, [size[0], 0])
const br = vec.add(point, size)
const bl = vec.add(point, [0, size[1]])
const intersections: Intersection[] = []
const topIntersection = intersectArcLineSegment(
start,
end,
center,
radius,
tl,
tr
)
const rightIntersection = intersectArcLineSegment(
start,
end,
center,
radius,
tr,
br
)
const bottomIntersection = intersectArcLineSegment(
start,
end,
center,
radius,
bl,
br
)
const leftIntersection = intersectArcLineSegment(
start,
end,
center,
radius,
tl,
bl
)
if (topIntersection.didIntersect) {
intersections.push({ ...topIntersection, message: 'top' })
}
if (rightIntersection.didIntersect) {
intersections.push({ ...rightIntersection, message: 'right' })
}
if (bottomIntersection.didIntersect) {
intersections.push({ ...bottomIntersection, message: 'bottom' })
}
if (leftIntersection.didIntersect) {
intersections.push({ ...leftIntersection, message: 'left' })
}
return intersections
}
/* -------------------------------------------------- */
/* Shape vs. Bounds */
/* -------------------------------------------------- */
export function intersectCircleBounds(
c: number[],
r: number,
bounds: Bounds
): Intersection[] {
const { minX, minY, width, height } = bounds
return intersectCircleRectangle(c, r, [minX, minY], [width, height])
}
export function intersectEllipseBounds(
c: number[],
rx: number,
ry: number,
bounds: Bounds,
rotation = 0
): Intersection[] {
const { minX, minY, width, height } = bounds
return intersectEllipseRectangle(
c,
rx,
ry,
[minX, minY],
[width, height],
rotation
)
}
export function intersectLineSegmentBounds(
a1: number[],
a2: number[],
bounds: Bounds
): Intersection[] {
const { minX, minY, width, height } = bounds
return intersectRectangleLineSegment([minX, minY], [width, height], a1, a2)
}
export function intersectPolylineBounds(
points: number[][],
bounds: Bounds
): Intersection[] {
const { minX, minY, width, height } = bounds
const intersections: Intersection[] = []
for (let i = 1; i < points.length; i++) {
intersections.push(
...intersectRectangleLineSegment(
[minX, minY],
[width, height],
points[i - 1],
points[i]
)
)
}
return intersections
}
export function intersectPolygonBounds(
points: number[][],
bounds: Bounds
): Intersection[] {
const { minX, minY, width, height } = bounds
const intersections: Intersection[] = []
for (let i = 1; i < points.length + 1; i++) {
intersections.push(
...intersectRectangleLineSegment(
[minX, minY],
[width, height],
points[i - 1],
points[i % points.length]
)
)
}
return intersections
}
export function intersectArcBounds(
start: number[],
end: number[],
center: number[],
radius: number,
bounds: Bounds
): Intersection[] {
const { minX, minY, width, height } = bounds
return intersectArcRectangle(
start,
end,
center,
radius,
[minX, minY],
[width, height]
)
}