forked from mirrors/0ad
elexis
a482f7bc1e
Thereby unify the chordal Catmull-Rom spline interpolation of the ClumpPlacer (C++bd53b14f58, JS0e0ed94926), the copy of that in the PathPlacer (bc805bd357, refs #892) and the centripetal Catmull-Rom spline of the bicubicInterpolation function from93aefe0787, refs #4218 and don't claim the latter to be a uniform Catmull-Rom spline. Reviewed in part by fatherbushido, discussed in93aefe0787. This was SVN commit r20383.
43 lines
1.4 KiB
JavaScript
43 lines
1.4 KiB
JavaScript
/**
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* Catmull-Rom spline.
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* Interpolates the value of a point that is located between four known equidistant points with given values by
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* constructing a polynomial of degree three that goes through all points.
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*
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* @param {Number} tension - determines the geometry of the curve, between 0 (tight curve) and 1 (smooth curve).
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* Depending on the tension, the spline is called uniform (0), centripetal (0.5) or chordal (1).
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* @param {Number} x - Location of the point to interpolate, relative to p1
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*/
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function cubicInterpolation(tension, x, p0, p1, p2, p3)
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{
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let P = -tension * p0 + (2 - tension) * p1 + (tension - 2) * p2 + tension * p3;
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let Q = 2 * tension * p0 + (tension - 3) * p1 + (3 - 2 * tension) * p2 - tension * p3;
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let R = -tension * p0 + tension * p2;
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let S = p1;
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return ((P * x + Q) * x + R) * x + S;
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}
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/**
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* Two dimensional interpolation within a square grid using a polynomial of degree three.
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*
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* @param {Number} x, y - Location of the point to interpolate, relative to p11
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*/
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function bicubicInterpolation
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(
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x, y,
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p00, p01, p02, p03,
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p10, p11, p12, p13,
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p20, p21, p22, p23,
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p30, p31, p32, p33
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)
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{
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let tension = 0.5;
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return cubicInterpolation(
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tension,
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x,
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cubicInterpolation(tension, y, p00, p01, p02, p03),
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cubicInterpolation(tension, y, p10, p11, p12, p13),
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cubicInterpolation(tension, y, p20, p21, p22, p23),
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cubicInterpolation(tension, y, p30, p31, p32, p33));
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}
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