240 lines
6.7 KiB
Go
240 lines
6.7 KiB
Go
package pixel
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import (
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"fmt"
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"math"
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"math/cmplx"
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"github.com/go-gl/mathgl/mgl64"
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)
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// Vec is a 2D vector type. It is unusually implemented as complex128 for convenience. Since
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// Go does not allow operator overloading, implementing vector as a struct leads to a bunch of
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// methods for addition, subtraction and multiplication of vectors. With complex128, much of
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// this functionality is given through operators.
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//
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// Create vectors with the V constructor:
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//
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// u := pixel.V(1, 2)
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// v := pixel.V(8, -3)
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//
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// Add and subtract them using the standard + and - operators:
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//
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// w := u + v
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// fmt.Println(w) // Vec(9, -1)
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// fmt.Println(u - v) // Vec(-7, 5)
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//
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// Additional standard vector operations can be obtained with methods:
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//
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// u := pixel.V(2, 3)
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// v := pixel.V(8, 1)
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// if u.X() < 0 {
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// fmt.Println("this won't happen")
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// }
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// x := u.Unit().Dot(v.Unit())
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type Vec complex128
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// V returns a new 2d vector with the given coordinates.
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func V(x, y float64) Vec {
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return Vec(complex(x, y))
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}
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// String returns the string representation of the vector u.
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//
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// u := pixel.V(4.5, -1.3)
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// u.String() // returns "Vec(4.5, -1.3)"
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// fmt.Println(u) // Vec(4.5, -1.3)
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func (u Vec) String() string {
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return fmt.Sprintf("Vec(%v, %v)", u.X(), u.Y())
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}
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// X returns the x coordinate of the vector u.
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func (u Vec) X() float64 {
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return real(u)
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}
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// Y returns the y coordinate of the vector u.
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func (u Vec) Y() float64 {
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return imag(u)
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}
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// XY returns the components of the vector in two return values.
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func (u Vec) XY() (x, y float64) {
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return real(u), imag(u)
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}
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// Len returns the length of the vector u.
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func (u Vec) Len() float64 {
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return cmplx.Abs(complex128(u))
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}
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// Angle returns the angle between the vector u and the x-axis. The result is in the range [-Pi, Pi].
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func (u Vec) Angle() float64 {
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return cmplx.Phase(complex128(u))
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}
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// Unit returns a vector of length 1 with the same angle as u.
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func (u Vec) Unit() Vec {
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return u / V(u.Len(), 0)
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}
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// Scaled returns the vector u multiplied by c.
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func (u Vec) Scaled(c float64) Vec {
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return u * V(c, 0)
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}
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// Rotated returns the vector u rotated by the given angle in radians.
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func (u Vec) Rotated(angle float64) Vec {
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sin, cos := math.Sincos(angle)
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return u * V(cos, sin)
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}
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// Dot returns the dot product of vectors u and v.
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func (u Vec) Dot(v Vec) float64 {
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return u.X()*v.X() + u.Y()*v.Y()
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}
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// Cross return the cross product of vectors u and v.
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func (u Vec) Cross(v Vec) float64 {
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return u.X()*v.Y() - v.X()*u.Y()
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}
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// Map applies the function f to both x and y components of the vector u and returns the modified
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// vector.
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func (u Vec) Map(f func(float64) float64) Vec {
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return V(
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f(u.X()),
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f(u.Y()),
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)
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}
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// Lerp returns a linear interpolation between vectors a and b.
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//
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// This function basically returns a point along the line between a and b and t chooses which point.
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// If t is 0, then a will be returned, if t is 1, b will be returned. Anything between 0 and 1 will
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// return the appropriate point between a and b and so on.
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func Lerp(a, b Vec, t float64) Vec {
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return a.Scaled(1-t) + b.Scaled(t)
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}
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// Rect is a 2D rectangle aligned with the axes of the coordinate system. It has a position
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// and a size.
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//
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// You can manipulate the position and the size using the usual vector operations.
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type Rect struct {
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Pos, Size Vec
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}
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// R returns a new Rect with given position (x, y) and size (w, h).
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func R(x, y, w, h float64) Rect {
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return Rect{
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Pos: V(x, y),
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Size: V(w, h),
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}
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}
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// String returns the string representation of the rectangle.
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//
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// r := pixel.R(100, 50, 200, 300)
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// r.String() // returns "Rect(100, 50, 200, 300)"
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// fmt.Println(r) // Rect(100, 50, 200, 300)
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func (r Rect) String() string {
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return fmt.Sprintf("Rect(%v, %v, %v, %v)", r.X(), r.Y(), r.W(), r.H())
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}
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// X returns the x coordinate of the position of the rectangle.
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func (r Rect) X() float64 {
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return r.Pos.X()
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}
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// Y returns the y coordinate of the position of the rectangle
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func (r Rect) Y() float64 {
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return r.Pos.Y()
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}
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// W returns the width of the rectangle.
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func (r Rect) W() float64 {
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return r.Size.X()
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}
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// H returns the height of the rectangle.
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func (r Rect) H() float64 {
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return r.Size.Y()
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}
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// XYWH returns all of the four components of the rectangle in four return values.
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func (r Rect) XYWH() (x, y, w, h float64) {
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return r.X(), r.Y(), r.W(), r.H()
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}
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// Center returns the position of the center of the rectangle.
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func (r Rect) Center() Vec {
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return r.Pos + r.Size.Scaled(0.5)
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}
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// Contains checks whether a vector u is contained within this Rect (including it's borders).
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func (r Rect) Contains(u Vec) bool {
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min, max := r.Pos, r.Pos+r.Size
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return min.X() <= u.X() && u.X() <= max.X() && min.Y() <= u.Y() && u.Y() <= max.Y()
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}
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// Matrix is a 3x3 transformation matrix that can be used for all kinds of spacial transforms, such
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// as movement, scaling and rotations.
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//
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// Matrix has a handful of useful methods, each of which adds a transformation to the matrix. For
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// example:
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//
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// pixel.ZM.Move(pixel.V(100, 200)).Rotate(0, math.Pi/2)
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//
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// This code creates a Matrix that first moves everything by 100 units horizontaly and 200 units
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// vertically and then rotates everything by 90 degrees around the origin.
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type Matrix [9]float64
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// ZM stands for Zero-Matrix which is the identity matrix. Does nothing, no transformation.
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var ZM = Matrix(mgl64.Ident3())
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// Move moves everything by the delta vector.
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func (m Matrix) Move(delta Vec) Matrix {
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m3 := mgl64.Mat3(m)
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m3 = mgl64.Translate2D(delta.XY()).Mul3(m3)
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return Matrix(m3)
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}
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// ScaleXY scales everything around a given point by the scale factor in each axis respectively.
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func (m Matrix) ScaleXY(around Vec, scale Vec) Matrix {
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m3 := mgl64.Mat3(m)
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m3 = mgl64.Translate2D((-around).XY()).Mul3(m3)
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m3 = mgl64.Scale2D(scale.XY()).Mul3(m3)
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m3 = mgl64.Translate2D(around.XY()).Mul3(m3)
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return Matrix(m3)
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}
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// Scale scales everything around a given point by the scale factor.
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func (m Matrix) Scale(around Vec, scale float64) Matrix {
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return m.ScaleXY(around, V(scale, scale))
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}
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// Rotate rotates everything around a given point by the given angle in radians.
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func (m Matrix) Rotate(around Vec, angle float64) Matrix {
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m3 := mgl64.Mat3(m)
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m3 = mgl64.Translate2D((-around).XY()).Mul3(m3)
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m3 = mgl64.Rotate3DZ(angle).Mul3(m3)
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m3 = mgl64.Translate2D(around.XY()).Mul3(m3)
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return Matrix(m3)
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}
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// Project applies all transformations added to the Matrix to a vector u and returns the result.
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func (m Matrix) Project(u Vec) Vec {
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m3 := mgl64.Mat3(m)
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proj := m3.Mul3x1(mgl64.Vec3{u.X(), u.Y(), 1})
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return V(proj.X(), proj.Y())
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}
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// Unproject does the inverse operation to Project.
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func (m Matrix) Unproject(u Vec) Vec {
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m3 := mgl64.Mat3(m)
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inv := m3.Inv()
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unproj := inv.Mul3x1(mgl64.Vec3{u.X(), u.Y(), 1})
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return V(unproj.X(), unproj.Y())
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}
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