66 lines
1.9 KiB
JavaScript
66 lines
1.9 KiB
JavaScript
/*
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* Returns the point at which two lines, p and q, intersect or returns
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* undefined if they do not intersect.
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*/
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function intersectLine (p1, p2, q1, q2) {
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// Algorithm from J. Avro, (ed.) Graphics Gems, No 2, Morgan Kaufmann, 1994,
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// p7 and p473.
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// Compute a1, b1, c1, where line joining points 1 and 2 is F(x,y) = a1 x +
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// b1 y + c1 = 0.
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const a1 = p2.y - p1.y
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const b1 = p1.x - p2.x
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const c1 = (p2.x * p1.y) - (p1.x * p2.y)
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// Compute r3 and r4.
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const r3 = ((a1 * q1.x) + (b1 * q1.y) + c1)
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const r4 = ((a1 * q2.x) + (b1 * q2.y) + c1)
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// Check signs of r3 and r4. If both point 3 and point 4 lie on
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// same side of line 1, the line segments do not intersect.
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if ((r3 !== 0) && (r4 !== 0) && sameSign(r3, r4)) {
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return /* DONT_INTERSECT */
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}
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// Compute a2, b2, c2 where line joining points 3 and 4 is G(x,y) = a2 x + b2 y + c2 = 0
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const a2 = q2.y - q1.y
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const b2 = q1.x - q2.x
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const c2 = (q2.x * q1.y) - (q1.x * q2.y)
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// Compute r1 and r2
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const r1 = (a2 * p1.x) + (b2 * p1.y) + c2
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const r2 = (a2 * p2.x) + (b2 * p2.y) + c2
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// Check signs of r1 and r2. If both point 1 and point 2 lie
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// on same side of second line segment, the line segments do
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// not intersect.
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if ((r1 !== 0) && (r2 !== 0) && (sameSign(r1, r2))) {
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return /* DONT_INTERSECT */
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}
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// Line segments intersect: compute intersection point.
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const denom = (a1 * b2) - (a2 * b1)
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if (denom === 0) {
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return /* COLLINEAR */
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}
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const offset = Math.abs(denom / 2)
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// The denom/2 is to get rounding instead of truncating. It
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// is added or subtracted to the numerator, depending upon the
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// sign of the numerator.
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let num = (b1 * c2) - (b2 * c1)
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const x = (num < 0) ? ((num - offset) / denom) : ((num + offset) / denom)
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num = (a2 * c1) - (a1 * c2)
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const y = (num < 0) ? ((num - offset) / denom) : ((num + offset) / denom)
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return { x, y }
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}
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function sameSign (r1, r2) {
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return r1 * r2 > 0
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}
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export default intersectLine
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