Vector

Collection of generic, immutable vector math functions I've written overtime for different hobby projects.

API

Function	Vector2	Vector3	Vector4	Description
Abs	✅	✅	✅	Returns a vector with each component's absolute value
Add	✅	✅	✅	Component Wise Addition
Angle	✅	✅		Returns the angle between two vectors
Ceil	✅	✅	✅	Ceils each vectors component to the nearest integer
Clamp	✅	✅	✅	Clamps each component between two values
ContainsNaN	✅	✅	✅	Returns true if any component of the vector is NaN
Cross		✅		Returns the cross product between two vectors
Dot	✅	✅	✅	Returns the dot product between two vectors
Flip	✅	✅	✅	Scales the vector by -1
FlipX	✅	✅	✅	Returns a vector with the X component multiplied by -1
FlipY	✅	✅	✅	Returns a vector with the Y component multiplied by -1
FlipZ		✅	✅	Returns a vector with the Z component multiplied by -1
FlipW			✅	Returns a vector with the W component multiplied by -1
Floor	✅	✅	✅	Floors each vectors component
Format	✅	✅	✅	Build a string with vector data
Length	✅	✅	✅	Returns the length of the vector
LengthSquared	✅	✅	✅	Returns the squared length of the vector
Max	✅	✅	✅	Returns a new vector where each component is the largest value between the two vectors
MaxX	✅	✅	✅	Returns the largest X component between the two vectors
MaxY	✅	✅	✅	Returns the largest Y component between the two vectors
MaxZ		✅	✅	Returns the largest Z component between the two vectors
MaxW			✅	Returns the largest W component between the two vectors
MaxComponent	✅	✅	✅	Returns the vectors largest component
Midpoint	✅	✅	✅	Finds the mid point between two vectors
Min	✅	✅	✅	Returns a new vector where each component is the smallest value between the two vectors
MinX	✅	✅	✅	Returns the smallest X component between the two vectors
MinY	✅	✅	✅	Returns the smallest Y component between the two vectors
MinZ		✅	✅	Returns the smallest Z component between the two vectors
MinW			✅	Returns the smallest W component between the two vectors
MinComponent	✅	✅	✅	Returns the vectors smallest component
Normalized	✅	✅	✅	Returns the normalized vector
NearZero	✅	✅	✅	Returns true if all of the components are near 0
Round	✅	✅	✅	Rounds each vectors component to the nearest integer
Scale	✅	✅	✅	Scales the vector by some constant
Sqrt	✅	✅	✅	Returns a vector with each component's square root
Sub	✅	✅	✅	Component Wise Subtraction
Values	✅	✅	✅	Returns all components of the vector
X	✅	✅	✅	Returns the x component of the vector
Y	✅	✅	✅	Returns the y component of the vector
Z		✅	✅	Returns the z component of the vector
W			✅	Returns the w component of the vector
XY		✅	✅	Equivalent to vector2.New[T](v.x, v.y)
YZ		✅	✅	Equivalent to vector2.New[T](v.y, v.z)
XZ		✅	✅	Equivalent to vector2.New[T](v.x, v.z)
YX	✅	✅	✅	Equivalent to vector2.New[T](v.y, v.x)
ZX		✅	✅	Equivalent to vector2.New[T](v.z, v.x)
ZY		✅	✅	Equivalent to vector2.New[T](v.z, v.y)
Log	✅	✅	✅	Returns the natural logarithm for each component
Log2	✅	✅	✅	Returns the binary logarithm for each component
Log10	✅	✅	✅	Returns the decimal logarithm for each component
Exp	✅	✅	✅	Returns e**x, the base-e exponential for each component
Exp2	✅	✅	✅	Returns 2**x, the base-2 exponential for each component
Expm1	✅	✅	✅	Returns e**x - 1, the base-e exponential for each component minus 1. It is more accurate than Exp(x) - 1 when the component is near zero
Write	✅	✅	✅	Write vector component data as binary to io.Writer

Example

Below is an example on how to implement the different sign distance field functions in a generic fashion to work for both int8, int16, int32 int, int64, float32, and float64.

The code below produces this output:

package main

import (
	"fmt"
	"image"
	"image/color"
	"image/png"
	"math"
	"os"

	"github.com/EliCDavis/vector"
	"github.com/EliCDavis/vector/vector2"
	"github.com/EliCDavis/vector/vector3"
)

type Field[T vector.Number] func(v vector3.Vector[T]) float64

func Sphere[T vector.Number](pos vector3.Vector[T], radius float64) Field[T] {
	return func(v vector3.Vector[T]) float64 {
		return v.Distance(pos) - radius
	}
}

func Box[T vector.Number](pos vector3.Vector[T], bounds vector3.Vector[T]) Field[T] {
	halfBounds := bounds.Scale(0.5)
	// It's best to watch the video to understand
	// https://www.youtube.com/watch?v=62-pRVZuS5c
	return func(v vector3.Vector[T]) float64 {
		q := v.Sub(pos).Abs().Sub(halfBounds)
		inside := math.Min(float64(q.MaxComponent()), 0)
		return vector3.Max(q, vector3.Zero[T]()).Length() + inside
	}
}

func Union[T vector.Number](fields ...Field[T]) Field[T] {
	return func(v vector3.Vector[T]) float64 {
		min := math.MaxFloat64

		for _, f := range fields {
			fv := f(v)
			if fv < min {
				min = fv
			}
		}

		return min
	}
}

func Intersect[T vector.Number](fields ...Field[T]) Field[T] {
	return func(v vector3.Vector[T]) float64 {
		max := -math.MaxFloat64

		for _, f := range fields {
			fv := f(v)
			if fv > max {
				max = fv
			}
		}

		return max
	}
}

func Subtract[T vector.Number](minuend, subtrahend Field[T]) Field[T] {
	return func(f vector3.Vector[T]) float64 {
		return math.Max(minuend(f), -subtrahend(f))
	}
}

func Translate[T vector.Number](field Field[T], translation vector3.Vector[T]) Field[T] {
	return func(v vector3.Vector[T]) float64 {
		return field(v.Sub(translation))
	}
}

func evaluateAtDepth[T vector.Number](dimension int, field Field[T], depth T, i int) {
	img := image.NewRGBA(image.Rectangle{
		image.Point{0, 0},
		image.Point{dimension, dimension},
	})

	for x := 0; x < dimension; x++ {
		for y := 0; y < dimension; y++ {
			v := field(vector3.New[T](T(x), T(y), depth))
			byteVal := (v / float64(dimension/20)) * 255
			var c color.Color
			if v > 0 {
				c = color.RGBA{R: 0, G: 0, B: byte(byteVal), A: 255}
			} else {
				c = color.RGBA{R: 0, G: byte(-byteVal), B: 0, A: 255}
			}
			img.Set(x, y, c)
		}
	}

	f, err := os.Create(fmt.Sprintf("field_%04d.png", i))
	if err != nil {
		panic(err)
	}
	defer f.Close()

	err = png.Encode(f, img)
	if err != nil {
		panic(err)
	}
}

func main() {
	dimension := 512
	quarterDim := float64(dimension) / 4.

	middleCoord := vector2.
		Fill(dimension).
		Scale(0.5).
		ToFloat64()

	middleCord3D := vector3.New(middleCoord.X(), middleCoord.Y(), 0)

	smallRing := Subtract(
		Sphere(middleCord3D, 100),
		Sphere(middleCord3D, 50),
	)

	field := Intersect(
		Subtract(
			Sphere(middleCord3D, 200),
			Sphere(middleCord3D, 100),
		),
		Union(
			Translate(smallRing, vector3.New(1., 1., 0.).Scale(quarterDim)),
			Translate(smallRing, vector3.New(1., -1., 0.).Scale(quarterDim)),
			Translate(smallRing, vector3.New(-1., 1., 0.).Scale(quarterDim)),
			Translate(smallRing, vector3.New(-1., -1., 0.).Scale(quarterDim)),
			Box(middleCord3D, middleCord3D),
		),
	)

	for i := 0; i < 100; i++ {
		evaluateAtDepth(dimension, field, float64(-dimension/2)+(float64(i*dimension)*0.01), i)
	}
}