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[wpimath] Clean up math comments (#4252)

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This commit is contained in:
Tyler Veness
2022-05-20 15:16:56 -07:00
committed by GitHub
parent fff4d1f44e
commit 5aa67f56e6
25 changed files with 141 additions and 132 deletions
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26
wpimath/src/main/native/include/frc/spline/CubicHermiteSpline.h
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@@ -51,25 +51,25 @@ class WPILIB_DLLEXPORT CubicHermiteSpline : public Spline<3> {
*/
static Matrixd<4, 4> MakeHermiteBasis() {
// Given P(i), P'(i), P(i+1), P'(i+1), the control vectors, we want to find
// the coefficients of the spline P(t) = a3 * t^3 + a2 * t^2 + a1 * t + a0.
// the coefficients of the spline P(t) = a₃t³ + a₂t² + a₁t + a₀.
//
// P(i) = P(0) = a0
// P'(i) = P'(0) = a1
// P(i+1) = P(1) = a3 + a2 + a1 + a0
// P'(i+1) = P'(1) = 3 * a3 + 2 * a2 + a1
// P(i) = P(0) = a₀
// P'(i) = P'(0) = a₁
// P(i+1) = P(1) = a₃ + a₂ + a₁ + a₀
// P'(i+1) = P'(1) = 3a₃ + 2a₂ + a₁
//
// [ P(i) ] = [ 0 0 0 1 ][ a3 ]
// [ P'(i) ] = [ 0 0 1 0 ][ a2 ]
// [ P(i+1) ] = [ 1 1 1 1 ][ a1 ]
// [ P'(i+1) ] = [ 3 2 1 0 ][ a0 ]
// [P(i) ] = [0 0 0 1][a₃]
// [P'(i) ] = [0 0 1 0][a₂]
// [P(i+1) ] = [1 1 1 1][a₁]
// [P'(i+1)] = [3 2 1 0][a₀]
//
// To solve for the coefficients, we can invert the 4x4 matrix and move it
// to the other side of the equation.
//
// [ a3 ] = [ 2 1 -2 1 ][ P(i) ]
// [ a2 ] = [ -3 -2 3 -1 ][ P'(i) ]
// [ a1 ] = [ 0 1 0 0 ][ P(i+1) ]
// [ a0 ] = [ 1 0 0 0 ][ P'(i+1) ]
// [a₃] = [ 2 1 -2 1][P(i) ]
// [a₂] = [-3 -2 3 -1][P'(i) ]
// [a₁] = [ 0 1 0 0][P(i+1) ]
// [a₀] = [ 1 0 0 0][P'(i+1)]
static const Matrixd<4, 4> basis{{+2.0, +1.0, -2.0, +1.0},
{-3.0, -2.0, +3.0, -1.0},