Quadratic interpolation constructs a degree-two polynomial through three specified values. For points at 0, 0.5, and 1, solve the three point-on-curve equations, then evaluate the resulting polynomial at any intermediate x. section 8.1.2
A reusable quadratic interpolant
For values z1, z2, and z3, use P2(z1, z2, z3, x) = ax² + bx + c, where a = 2z1 − 4z2 + 2z3, b = −3z1 + 4z2 − z3, and c = z1. Applying this along three y-oriented lines and interpolating those results along x produces a biquadratic surface. section 8.1.2
Use quadratic interpolation when:
- Three values determine an unambiguous single-variable quadratic. section 8.5
- A higher-dimensional surface can be built by repeating one-dimensional interpolation along each coordinate. section 8.1.2
- A polynomial approximation is acceptable; exact cylindrical geometry requires rational splines such as NURBS. section 8.5
