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35 lines
No EOL
917 B
JavaScript
35 lines
No EOL
917 B
JavaScript
import {newtonIterationsOnInterval} from '../curves/newtonIterations';
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export function surfaceSurfaceStablePoints(surfaceA, surfaceB) {
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function impl(curve) {
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//solving minimization problem of squared distance
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//f(u) = (fx(u) - x)^2 + (fy(u) - y)^2 + (fz(u) - z)^2 = fx^2 - 2*fx*x + x^2 ...
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//f'(u) = 2*fx*f'x - 2*x*f'x ...
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//f''(u) = 2*fx*f''x + 2*f'x*f'x - 2*x*f''x...
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const X=0, Y=1, Z=2;
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function squareDistanceFn(u) {
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let [f, d1, d2] = curve.eval(u, 2);
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let r1Comp = i => 2 * f[i] * d1[i] - 2 * f[i] * d1[i];
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let r2Comp = i => 2 * f[i] * d2[i] + 2 * d1[i] * d1[i] - 2 * f[i] * d2[i];
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let r1 = r1Comp(X) + r1Comp(Y) + r1Comp(Z);
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let r2 = r2Comp(X) + r2Comp(Y) + r2Comp(Z);
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return [r1, r2];
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}
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let intMin = 0;
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let intMax = 0;
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return newtonIterationsOnInterval(squareDistanceFn, intMin, intMax, 1e-5);
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}
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} |