39 template <typename S, typename T>
40 class Interpolator : public std::map<S, T> {
54     std::pair<S, T> first() const {  in first()
58     std::pair<S, T> last() const {  in last()
63     T findY(S x) { // logically const, but modifies cache  in findY()
89             const S interval =  high->first - low->first;  in findY()
93                 const S t = (x - low->first) / interval;  in findY()
94                 const S t2 = t * t;  in findY()
125             S sec, sec0, sec1;  in findY()
137             S m0, m1;  in findY()
159                 const S maxSlope = 3 * sec;  in findY()
167             const S t = (x - low->first) / interval;  in findY()
168             const S t2 = t * t;  in findY()
174                 const S c0 = low->second;  in findY()
175                 const S c1 = m0;  in findY()
176                 const S c2 = 3 * dy - 2 * m0 - m1;  in findY()
177                 const S c3 = m0 + m1 - 2 * dy;  in findY()
182                 const S t3 = t2 * t;  in findY()
183                 const S h00 =  2 * t3 - 3 * t2     + 1;  in findY()
184                 const S h10 =      t3 - 2 * t2 + t    ;  in findY()
185                 const S h01 = -2 * t3 + 3 * t2        ;  in findY()
186                 const S h11 =      t3     - t2        ;  in findY()
311     static S constrainSlope(S slope, S maxSlope) {  in constrainSlope()
314             slope = std::max(slope, S(0)); // not globally monotonic  in constrainSlope()
317             slope = std::min(slope, S(0)); // not globally monotonic  in constrainSlope()
326     S mFirstSlope;
327     S mLastSlope;
330     std::unordered_map<S, std::tuple<S /* c1 */, S /* c2 */, S /* c3 */>> mMemo;