// Build splines based on quadratics
// Does curve fitting witih quadratics for the form:
// a*x*x + b*x + c = y
// 1. First Segment - (x0, y0),(x1, y1)
// a. Assume a == 0
// b. Set up the first two points
// c. Compute first derivative (slope) y'[1]
// d. Plot (will be a line)
// 2. For points i = 2; i < n; i++
// a. Use known derivative from previous step
// b. a*x[i-1]*x[i-1] + b*x[i-1] + c = y[i-1]
// c. a*x[i]*x[i] + b*x[i] + c = y[i]
// d. 2*a*x[i-1] + b = y'[i-1]
// e. Solve equations.
// f. y'[i] ;= 2*a*x[i] + b
// g. plot
func (d *Doodle) GraphQuadSpline(list List) {
bug.Where()
n := len(list)
m := make(Matrix, 3)
bug.Pd("n", n)
m[0] = FillPoly(list[0], 3)
m[1] = FillPoly(list[1], 3)
m[2] = FirstSlope()
fmt.Printf("m=%v\n", m)
v := m.GaussianElimination()
fmt.Printf("m=%v\n", m)
fmt.Printf("v=%v\n", v)
d.Plot(func(x float64) float64 {
return Poly(v, x)
}, list[0].X, list[1].X)
for i := 2; i < n; i++ {
m[0] = FillPoly(list[i-1], 3)
m[1] = FillPoly(list[i], 3)
m[2] = Derivative(list[i-1].X, v[0], v[1])
fmt.Printf("m=%v\n", m)
v = m.GaussianElimination()
fmt.Printf("m=%v\n", m)
fmt.Printf("v=%v\n", v)
d.Plot(func(x float64) float64 {
return Poly(v, x)
}, list[i-1].X, list[i].X)
}
}
// Build splines based on cubic equations - attempt A
// The four equations are:
// 1. cubic(x-1)
// 2. cubic(x)
// 3. cubic(x+1)
// 4. 1st derivative
func (d *Doodle) GraphCubicSplineA(list List) {
bug.Where()
n := len(list)
m := make(Matrix, 4)
bug.Pd("n", n)
m[0] = FillPoly(list[0], 4)
m[1] = FillPoly(list[1], 4)
m[2] = FillPoly(list[2], 4)
m[3] = FillPoly(list[3], 4)
fmt.Printf("m=%v\n", m)
v := m.GaussianElimination()
fmt.Printf("m=%v\n", m)
fmt.Printf("v=%v\n", v)
d.Plot(func(x float64) float64 {
return Poly(v, x)
}, list[0].X, list[1].X)
for i := 2; i < n-1; i++ {
m[0] = FillPoly(list[i-1], 4)
m[1] = FillPoly(list[i], 4)
m[2] = FillPoly(list[i+1], 4)
m[3] = FirstDerivativeA(list[i-1].X, v[0], v[1], v[2])
//m[2] = FirstDerivative(list[i-1].X, v[0], v[1], v[2])
//m[3] = SecondDerivative(list[i-1].X, v[0], v[1])
fmt.Printf("m=%v\n", m)
v = m.GaussianElimination()
fmt.Printf("m=%v\n", m)
fmt.Printf("v=%v\n", v)
d.Plot(func(x float64) float64 {
return Poly(v, x)
}, list[i-1].X, list[i].X)
}
}