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import type {
ConstructionState,
ConstructionElement,
ConstructionPoint,
ConstructionCircle,
ConstructionSegment,
IntersectionCandidate,
} from '../types'
import { getPoint, getSegment, getRadius, getAllCircles, getAllSegments } from './constructionState'
const TOLERANCE = 0.001
interface Vec2 {
x: number
y: number
}
// ── Primitive intersections ────────────────────────────────────────
export function circleCircleIntersections(
c1x: number,
c1y: number,
c1r: number,
c2x: number,
c2y: number,
c2r: number
): Vec2[] {
const fc1 = new Flatten.Circle(new Flatten.Point(c1x, c1y), c1r)
const fc2 = new Flatten.Circle(new Flatten.Point(c2x, c2y), c2r)
const pts = fc1.intersect(fc2)
return pts.map((p: Flatten.Point) => ({ x: p.x, y: p.y }))
}
export function circleSegmentIntersections(
cx: number,
cy: number,
cr: number,
x1: number,
y1: number,
x2: number,
y2: number
): Vec2[] {
const fc = new Flatten.Circle(new Flatten.Point(cx, cy), cr)
const fs = new Flatten.Segment(new Flatten.Point(x1, y1), new Flatten.Point(x2, y2))
const pts = fc.intersect(fs)
return pts.map((p: Flatten.Point) => ({ x: p.x, y: p.y }))
}
/** Circle ∩ infinite line through two points (for "produced" segments — Post.2) */
export function circleLineIntersections(
cx: number,
cy: number,
cr: number,
x1: number,
y1: number,
x2: number,
y2: number
): Vec2[] {
// Degenerate: two identical points can't define a line
if (Math.abs(x1 - x2) < TOLERANCE && Math.abs(y1 - y2) < TOLERANCE) return []
const fc = new Flatten.Circle(new Flatten.Point(cx, cy), cr)
const fl = new Flatten.Line(new Flatten.Point(x1, y1), new Flatten.Point(x2, y2))
const pts = fc.intersect(fl)
return pts.map((p: Flatten.Point) => ({ x: p.x, y: p.y }))
}
export function segmentSegmentIntersection(
a1x: number,
a1y: number,
a2x: number,
a2y: number,
b1x: number,
b1y: number,
b2x: number,
b2y: number
): Vec2[] {
const sa = new Flatten.Segment(new Flatten.Point(a1x, a1y), new Flatten.Point(a2x, a2y))
const sb = new Flatten.Segment(new Flatten.Point(b1x, b1y), new Flatten.Point(b2x, b2y))
const pts = sa.intersect(sb)
return pts.map((p: Flatten.Point) => ({ x: p.x, y: p.y }))
}
// ── High-level: find new intersections for a newly added element ───
function isDuplicate(
candidate: Vec2,
existing: IntersectionCandidate[],
statePoints: Vec2[]
): boolean {
for (const e of existing) {
if (Math.abs(candidate.x - e.x) < TOLERANCE && Math.abs(candidate.y - e.y) < TOLERANCE) {
return true
}
}
for (const p of statePoints) {
if (Math.abs(candidate.x - p.x) < TOLERANCE && Math.abs(candidate.y - p.y) < TOLERANCE) {
return true
}
}
return false
}
function getCircleData(state: ConstructionState, c: ConstructionCircle) {
const center = getPoint(state, c.centerId)
const r = getRadius(state, c.id)
return center && r > 0 ? { cx: center.x, cy: center.y, r } : null
}
function getSegmentData(state: ConstructionState, s: ConstructionSegment) {
const from = getPoint(state, s.fromId)
const to = getPoint(state, s.toId)
return from && to ? { x1: from.x, y1: from.y, x2: to.x, y2: to.y } : null
}
/** Is (cx, cy) at one of the segment's endpoints? */
function isEndpoint(
cx: number,
cy: number,
seg: { x1: number; y1: number; x2: number; y2: number }
): boolean {
return (
(Math.abs(cx - seg.x1) < TOLERANCE && Math.abs(cy - seg.y1) < TOLERANCE) ||
(Math.abs(cx - seg.x2) < TOLERANCE && Math.abs(cy - seg.y2) < TOLERANCE)
)
}
/** Return points from `linePts` that aren't already in `segPts`. */
function removeAlreadyFound(linePts: Vec2[], segPts: Vec2[]): Vec2[] {
return linePts.filter(
(lp) =>
!segPts.some((sp) => Math.abs(lp.x - sp.x) < TOLERANCE && Math.abs(lp.y - sp.y) < TOLERANCE)
)
}
/**
* Check if a candidate intersection point is "beyond" a specified point
* on a segment — i.e. on the extension past that endpoint.
*
* Uses dot product: candidate is "beyond" P (away from Q) when
* dot(candidate − P, P − Q) > 0.
*/
export function isCandidateBeyondPoint(
candidate: { x: number; y: number },
beyondId: string,
ofA: string,
ofB: string,
state: ConstructionState
): boolean {
// Find which of ofA/ofB is the segment
const segId = [ofA, ofB].find((id) => id.startsWith('seg-'))
if (!segId) return true // no segment involved, can't check
const seg = getSegment(state, segId)
if (!seg) return true
const beyondPt = getPoint(state, beyondId)
if (!beyondPt) return true
const fromPt = getPoint(state, seg.fromId)
const toPt = getPoint(state, seg.toId)
if (!fromPt || !toPt) return true
// Determine which endpoint is the "beyond" point and which is the "other"
const isBeyondFrom =
Math.abs(beyondPt.x - fromPt.x) < TOLERANCE && Math.abs(beyondPt.y - fromPt.y) < TOLERANCE
const otherPt = isBeyondFrom ? toPt : fromPt
// dot(candidate − beyondPt, beyondPt − otherPt) > 0
const dx = beyondPt.x - otherPt.x
const dy = beyondPt.y - otherPt.y
const cx = candidate.x - beyondPt.x
const cy = candidate.y - beyondPt.y
return dx * cx + dy * cy > 0
}
export function findNewIntersections(
state: ConstructionState,
newElement: ConstructionElement,
existingCandidates: IntersectionCandidate[],
extendSegments: boolean = false
): IntersectionCandidate[] {
if (newElement.kind === 'point') return []
const statePoints = state.elements
.filter((e): e is ConstructionPoint => e.kind === 'point')
.map((p) => ({ x: p.x, y: p.y }))
const results: IntersectionCandidate[] = []
function addCandidates(pts: Vec2[], idA: string, idB: string) {
pts.forEach((pt, i) => {
if (!isDuplicate(pt, [...existingCandidates, ...results], statePoints)) {
results.push({ x: pt.x, y: pt.y, ofA: idA, ofB: idB, which: i })
}
})
}
if (newElement.kind === 'circle') {
const newData = getCircleData(state, newElement)
if (!newData) return []
// vs all existing circles
for (const c of getAllCircles(state)) {
if (c.id === newElement.id) continue
const d = getCircleData(state, c)
if (!d) continue
const pts = circleCircleIntersections(newData.cx, newData.cy, newData.r, d.cx, d.cy, d.r)
addCandidates(pts, newElement.id, c.id)
}
// vs all existing segments
for (const s of getAllSegments(state)) {
const d = getSegmentData(state, s)
if (!d) continue
// Always compute finite segment intersections
const segPts = circleSegmentIntersections(
newData.cx,
newData.cy,
newData.r,
d.x1,
d.y1,
d.x2,
d.y2
)
addCandidates(segPts, newElement.id, s.id)
// Additionally check line extension if the circle's center is at a segment endpoint
// (Euclid's Post.2: "produce" a finite straight line beyond its endpoint)
if (
extendSegments &&
(s.origin === 'straightedge' || s.origin === 'given') &&
isEndpoint(newData.cx, newData.cy, d)
) {
const linePts = circleLineIntersections(
newData.cx,
newData.cy,
newData.r,
d.x1,
d.y1,
d.x2,
d.y2
)
const extensionPts = removeAlreadyFound(linePts, segPts)
addCandidates(extensionPts, newElement.id, s.id)
}
}
} else if (newElement.kind === 'segment') {
const newData = getSegmentData(state, newElement)
if (!newData) return []
// vs all existing circles
for (const c of getAllCircles(state)) {
const d = getCircleData(state, c)
if (!d) continue
// Always compute finite segment intersections
const segPts = circleSegmentIntersections(
d.cx,
d.cy,
d.r,
newData.x1,
newData.y1,
newData.x2,
newData.y2
)
addCandidates(segPts, newElement.id, c.id)
// Additionally check line extension if the circle's center is at a segment endpoint
if (
extendSegments &&
(newElement.origin === 'straightedge' || newElement.origin === 'given') &&
isEndpoint(d.cx, d.cy, newData)
) {
const linePts = circleLineIntersections(
d.cx,
d.cy,
d.r,
newData.x1,
newData.y1,
newData.x2,
newData.y2
)
const extensionPts = removeAlreadyFound(linePts, segPts)
addCandidates(extensionPts, newElement.id, c.id)
}
}
// vs all existing segments
for (const s of getAllSegments(state)) {
if (s.id === newElement.id) continue
const sd = getSegmentData(state, s)
if (!sd) continue
const pts = segmentSegmentIntersection(
newData.x1,
newData.y1,
newData.x2,
newData.y2,
sd.x1,
sd.y1,
sd.x2,
sd.y2
)
addCandidates(pts, newElement.id, s.id)
}
}
return results
}
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