tldraw/utils/vec.ts
2021-05-14 13:44:23 +01:00

479 lines
9.5 KiB
TypeScript

/**
* Clamp a value into a range.
* @param n
* @param min
*/
export function clamp(n: number, min: number): number
export function clamp(n: number, min: number, max: number): number
export function clamp(n: number, min: number, max?: number): number {
return Math.max(min, typeof max !== "undefined" ? Math.min(n, max) : n)
}
/**
* Negate a vector.
* @param A
*/
export function neg(A: number[]) {
return [-A[0], -A[1]]
}
/**
* Add vectors.
* @param A
* @param B
*/
export function add(A: number[], B: number[]) {
return [A[0] + B[0], A[1] + B[1]]
}
/**
* Add scalar to vector.
* @param A
* @param B
*/
export function addScalar(A: number[], n: number) {
return [A[0] + n, A[1] + n]
}
/**
* Subtract vectors.
* @param A
* @param B
*/
export function sub(A: number[], B: number[]) {
return [A[0] - B[0], A[1] - B[1]]
}
/**
* Subtract scalar from vector.
* @param A
* @param B
*/
export function subScalar(A: number[], n: number) {
return [A[0] - n, A[1] - n]
}
/**
* Get the vector from vectors A to B.
* @param A
* @param B
*/
export function vec(A: number[], B: number[]) {
// A, B as vectors get the vector from A to B
return [B[0] - A[0], B[1] - A[1]]
}
/**
* Vector multiplication by scalar
* @param A
* @param n
*/
export function mul(A: number[], n: number) {
return [A[0] * n, A[1] * n]
}
export function mulV(A: number[], B: number[]) {
return [A[0] * B[0], A[1] * B[1]]
}
/**
* Vector division by scalar.
* @param A
* @param n
*/
export function div(A: number[], n: number) {
return [A[0] / n, A[1] / n]
}
/**
* Vector division by vector.
* @param A
* @param n
*/
export function divV(A: number[], B: number[]) {
return [A[0] / B[0], A[1] / B[1]]
}
/**
* Perpendicular rotation of a vector A
* @param A
*/
export function per(A: number[]) {
return [A[1], -A[0]]
}
/**
* Dot product
* @param A
* @param B
*/
export function dpr(A: number[], B: number[]) {
return A[0] * B[0] + A[1] * B[1]
}
/**
* Cross product (outer product) | A X B |
* @param A
* @param B
*/
export function cpr(A: number[], B: number[]) {
return A[0] * B[1] - B[0] * A[1]
}
/**
* Length of the vector squared
* @param A
*/
export function len2(A: number[]) {
return A[0] * A[0] + A[1] * A[1]
}
/**
* Length of the vector
* @param A
*/
export function len(A: number[]) {
return Math.hypot(A[0], A[1])
}
/**
* Project A over B
* @param A
* @param B
*/
export function pry(A: number[], B: number[]) {
return dpr(A, B) / len(B)
}
/**
* Get normalized / unit vector.
* @param A
*/
export function uni(A: number[]) {
return div(A, len(A))
}
/**
* Get normalized / unit vector.
* @param A
*/
export function normalize(A: number[]) {
return uni(A)
}
/**
* Get the tangent between two vectors.
* @param A
* @param B
* @returns
*/
export function tangent(A: number[], B: number[]) {
return normalize(sub(A, B))
}
/**
* Dist length from A to B squared.
* @param A
* @param B
*/
export function dist2(A: number[], B: number[]) {
return len2(sub(A, B))
}
/**
* Dist length from A to B
* @param A
* @param B
*/
export function dist(A: number[], B: number[]) {
return Math.hypot(A[1] - B[1], A[0] - B[0])
}
/**
* A faster, though less accurate method for testing distances. Maybe faster?
* @param A
* @param B
* @returns
*/
export function fastDist(A: number[], B: number[]) {
const V = [B[0] - A[0], B[1] - A[1]]
const aV = [Math.abs(V[0]), Math.abs(V[1])]
let r = 1 / Math.max(aV[0], aV[1])
r = r * (1.29289 - (aV[0] + aV[1]) * r * 0.29289)
return [V[0] * r, V[1] * r]
}
/**
* Angle between vector A and vector B in radians
* @param A
* @param B
*/
export function ang(A: number[], B: number[]) {
return Math.atan2(cpr(A, B), dpr(A, B))
}
/**
* Angle between vector A and vector B in radians
* @param A
* @param B
*/
export function angle(A: number[], B: number[]) {
return Math.atan2(B[1] - A[1], B[0] - A[0])
}
/**
* Mean between two vectors or mid vector between two vectors
* @param A
* @param B
*/
export function med(A: number[], B: number[]) {
return mul(add(A, B), 0.5)
}
/**
* Vector rotation by r (radians)
* @param A
* @param r rotation in radians
*/
export function rot(A: number[], r: number) {
return [
A[0] * Math.cos(r) - A[1] * Math.sin(r),
A[0] * Math.sin(r) + A[1] * Math.cos(r),
]
}
/**
* Rotate a vector around another vector by r (radians)
* @param A vector
* @param C center
* @param r rotation in radians
*/
export function rotWith(A: number[], C: number[], r: number) {
if (r === 0) return A
const s = Math.sin(r)
const c = Math.cos(r)
const px = A[0] - C[0]
const py = A[1] - C[1]
const nx = px * c - py * s
const ny = px * s + py * c
return [nx + C[0], ny + C[1]]
}
/**
* Check of two vectors are identical.
* @param A
* @param B
*/
export function isEqual(A: number[], B: number[]) {
return A[0] === B[0] && A[1] === B[1]
}
/**
* Interpolate vector A to B with a scalar t
* @param A
* @param B
* @param t scalar
*/
export function lrp(A: number[], B: number[], t: number) {
return add(A, mul(vec(A, B), t))
}
/**
* Interpolate from A to B when curVAL goes fromVAL => to
* @param A
* @param B
* @param from Starting value
* @param to Ending value
* @param s Strength
*/
export function int(A: number[], B: number[], from: number, to: number, s = 1) {
const t = (clamp(from, to) - from) / (to - from)
return add(mul(A, 1 - t), mul(B, s))
}
/**
* Get the angle between the three vectors A, B, and C.
* @param p1
* @param pc
* @param p2
*/
export function ang3(p1: number[], pc: number[], p2: number[]) {
// this,
const v1 = vec(pc, p1)
const v2 = vec(pc, p2)
return ang(v1, v2)
}
/**
* Absolute value of a vector.
* @param A
* @returns
*/
export function abs(A: number[]) {
return [Math.abs(A[0]), Math.abs(A[1])]
}
export function rescale(a: number[], n: number) {
const l = len(a)
return [(n * a[0]) / l, (n * a[1]) / l]
}
/**
* Get whether p1 is left of p2, relative to pc.
* @param p1
* @param pc
* @param p2
*/
export function isLeft(p1: number[], pc: number[], p2: number[]) {
// isLeft: >0 for counterclockwise
// =0 for none (degenerate)
// <0 for clockwise
return (pc[0] - p1[0]) * (p2[1] - p1[1]) - (p2[0] - p1[0]) * (pc[1] - p1[1])
}
export function clockwise(p1: number[], pc: number[], p2: number[]) {
return isLeft(p1, pc, p2) > 0
}
const rounds = [1, 10, 100, 1000]
export function round(a: number[], d = 2) {
return [
Math.round(a[0] * rounds[d]) / rounds[d],
Math.round(a[1] * rounds[d]) / rounds[d],
]
}
/**
* Get the minimum distance from a point P to a line with a segment AB.
* @param A The start of the line.
* @param B The end of the line.
* @param P A point.
* @returns
*/
// export function distanceToLine(A: number[], B: number[], P: number[]) {
// const delta = sub(B, A)
// const angle = Math.atan2(delta[1], delta[0])
// const dir = rot(sub(P, A), -angle)
// return dir[1]
// }
/**
* Get the nearest point on a line segment AB.
* @param A The start of the line.
* @param B The end of the line.
* @param P A point.
* @param clamp Whether to clamp the resulting point to the segment.
* @returns
*/
// export function nearestPointOnLine(
// A: number[],
// B: number[],
// P: number[],
// clamp = true
// ) {
// const delta = sub(B, A)
// const length = len(delta)
// const angle = Math.atan2(delta[1], delta[0])
// const dir = rot(sub(P, A), -angle)
// if (clamp) {
// if (dir[0] < 0) return A
// if (dir[0] > length) return B
// }
// return add(A, div(mul(delta, dir[0]), length))
// }
/**
* Get the nearest point on a line with a known unit vector that passes through point A
* @param A Any point on the line
* @param u The unit vector for the line.
* @param P A point not on the line to test.
* @returns
*/
export function nearestPointOnLineThroughPoint(
A: number[],
u: number[],
P: number[]
) {
return add(A, mul(u, pry(sub(P, A), u)))
}
/**
* Distance between a point and a line with a known unit vector that passes through a point.
* @param A Any point on the line
* @param u The unit vector for the line.
* @param P A point not on the line to test.
* @returns
*/
export function distanceToLineThroughPoint(
A: number[],
u: number[],
P: number[]
) {
return dist(P, nearestPointOnLineThroughPoint(A, u, P))
}
/**
* Get the nearest point on a line segment between A and B
* @param A The start of the line segment
* @param B The end of the line segment
* @param P The off-line point
* @param clamp Whether to clamp the point between A and B.
* @returns
*/
export function nearestPointOnLineSegment(
A: number[],
B: number[],
P: number[],
clamp = true
) {
const delta = sub(B, A)
const length = len(delta)
const u = div(delta, length)
const pt = add(A, mul(u, pry(sub(P, A), u)))
if (clamp) {
const da = dist(A, pt)
const db = dist(B, pt)
if (db < da && da > length) return B
if (da < db && db > length) return A
}
return pt
}
/**
* Distance between a point and the nearest point on a line segment between A and B
* @param A The start of the line segment
* @param B The end of the line segment
* @param P The off-line point
* @param clamp Whether to clamp the point between A and B.
* @returns
*/
export function distanceToLineSegment(
A: number[],
B: number[],
P: number[],
clamp = true
) {
return dist(P, nearestPointOnLineSegment(A, B, P, clamp))
}
/**
* Get a vector d distance from A towards B.
* @param A
* @param B
* @param d
* @returns
*/
export function nudge(A: number[], B: number[], d: number) {
return add(A, mul(uni(vec(A, B)), d))
}