3bfa549e8b
- using std::string; - using std::wstring; - using std::ostream; - using std::istream; - using std::iostream; - using std::ostrstream; - using std::istrstream; - using std::fstream;
100 lines
2.4 KiB
C++
100 lines
2.4 KiB
C++
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//-----------------------------------------------------------------------------
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// tbezier.h: contains useful function to manipulate bezier polynomious
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//-----------------------------------------------------------------------------
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#ifndef TBEZIER_H
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#define TBEZIER_H
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#include <iterator>
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//-----------------------------------------------------------------------------
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/*!
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Compute the forward differences.
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*/
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template <class T>
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void forwardDifferences(
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const std::vector<T> &coeff,
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std::vector<T> &diffs)
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{
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diffs.clear();
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std::copy(coeff.begin(), coeff.end(), std::back_inserter(diffs));
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typename std::vector<T>::iterator vectIt;
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const UINT degree = coeff.size();
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for (UINT r = 0; r < degree; ++r) {
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vectIt = diffs.begin();
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std::advance(vectIt, r);
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std::adjacent_difference(vectIt, diffs.end(), vectIt);
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}
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}
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//-----------------------------------------------------------------------------
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/*!
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Converts Bezier form to power (polynomial) form.
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\par bez coefficients in Bezier form.
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\ret coeff coefficients of power form.
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\note coeffs are ordered from smaller b[0] to greater b[size-1] .
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*/
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template <class T>
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void bezier2poly(const std::vector<T> &bez,
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std::vector<T> &coeff)
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{
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forwardDifferences(bez, coeff); // compute forward differences
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// and store them in coeff.
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int
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degree = bez.size() - 1;
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double
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i_factorial = 1,
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n_r = 1;
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coeff[0] = bez[0];
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for (int i = 1; i < degree; i++) {
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i_factorial = i_factorial * i;
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n_r = n_r * (degree - i + 1);
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i_factorial = 1.0 / i_factorial;
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coeff[i] = (n_r * i_factorial) * coeff[i];
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}
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}
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//-----------------------------------------------------------------------------
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/*!
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Converts power (polynomial) form to Bezier form.
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\par coeff coefficients of power form.
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\ret bez coefficients in Bezier form.
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\note coeffs are ordered from smaller b[0] to greater b[size-1].
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*/
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template <class T>
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void poly2bezier(const std::vector<T> &poly,
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std::vector<T> &bez)
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{
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UINT n = poly.size();
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bez.clear();
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std::copy(poly.begin(), poly.end(), std::back_inserter(bez));
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double c, d, e;
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for (UINT j = 1; j < n; j++) {
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c = 1.0 / (n - j);
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d = 1;
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e = c;
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for (UINT i = n - 1; i >= j; i--) {
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bez[i] = d * bez[i] + e * bez[i - 1];
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d -= c;
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e += c;
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}
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}
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}
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#endif // TBEZIER_H
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//-----------------------------------------------------------------------------
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// End Of File
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//-----------------------------------------------------------------------------
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