Curve as a map [0,1] -> M

curve.go

package main



import (
	"math"
	"fmt"
)


func main() {

	circle := R3Circle{}
	fmt.Println("Points on a circle:")
	for i := 0.0; i < 1.0; i += 0.1 {
		pt := circle.f(i)
		fmt.Printf("x: %v, y: %v, z: %v\n", pt.coordinates()[0],
			pt.coordinates()[1], pt.coordinates()[2])
	}
	a, b := 0.1, 0.6
	chd := chord(circle, a, b)
	fmt.Println("Chord between points on the circle:")
	for _, pt := range chd {
		fmt.Printf("x: %v, y: %v, z: %v\n", pt.coordinates()[0],
			pt.coordinates()[1], pt.coordinates()[2])
	}

}

type curve interface {
	f(float64)point // continuous map [0,1] -> M
}

// point in M
type point interface {
	dim() int // dimension of the space
	coordinates() []float64
	increment(int, float64)point // increment along the given dimension
}


// Return the chord between two points on the curve
func chord(cv curve, a float64, b float64) []point {

	bcoord := cv.f(b).coordinates()
	acoord := cv.f(a).coordinates()

	diffcoord := make([]float64, cv.f(a).dim())
	diffsm := 0.0
	for i, _ := range bcoord {
		diffcoord[i] = bcoord[i] - acoord[i]
		diffsm += diffcoord[i]
	}



	// normalize to 0.1
	for i, _ := range diffcoord {
		diffcoord[i] /= math.Abs(diffsm)
		diffcoord[i] *= 0.1
	}


	chd := make([]point, 0)

	var pt point
	var distance float64
	pt = cv.f(a)
	chd = append(chd, pt)
	i := 0
	for {
		pt = chd[i].increment(0, 0)
		for j := 0; j < pt.dim(); j++ {
			pt = pt.increment(j, diffcoord[j])
		}
		chd = append(chd, pt)
		distance = 0.0
		for i, e := range pt.coordinates() {
			distance += math.Pow(e - bcoord[i], 2)
		}
		distance = math.Sqrt(distance)
		if distance <= 0.1 {
			break
		}
		i++
	}
	return chd
}


// Circle in R3
type R3Circle struct {

}

func (c R3Circle) f(a float64) point {

	values := make([]float64, 3)
	values[0] = math.Cos(2 * math.Pi * a)
	values[1] = math.Sin(2 * math.Pi * a)
	return R3Point{values: values}

}

type R3Point struct {
	values []float64
}

func(pt R3Point) dim() int {
	return 3
}

func (pt R3Point) coordinates() []float64 {
	return pt.values
}

func (pt R3Point) increment(i int, del float64) point {
	newValues := make([]float64, pt.dim())
	copy(newValues, pt.values)
	newValues[i] += del
	return R3Point{values: newValues}
}