99 lines
2.9 KiB
Go
99 lines
2.9 KiB
Go
package pixel
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import (
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"fmt"
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"math"
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)
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// Matrix is a 2x3 affine matrix that can be used for all kinds of spatial 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.IM.Moved(pixel.V(100, 200)).Rotated(pixel.ZV, math.Pi/2)
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//
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// This code creates a Matrix that first moves everything by 100 units horizontally and 200 units
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// vertically and then rotates everything by 90 degrees around the origin.
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//
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// Layout is:
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// [0] [2] [4]
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// [1] [3] [5]
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// 0 0 1 (implicit row)
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type Matrix [6]float64
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// IM stands for identity matrix. Does nothing, no transformation.
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var IM = Matrix{1, 0, 0, 1, 0, 0}
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// String returns a string representation of the Matrix.
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//
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// m := pixel.IM
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// fmt.Println(m) // Matrix(1 0 0 | 0 1 0)
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func (m Matrix) String() string {
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return fmt.Sprintf(
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"Matrix(%v %v %v | %v %v %v)",
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m[0], m[2], m[4],
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m[1], m[3], m[5],
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)
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}
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// Moved moves everything by the delta vector.
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func (m Matrix) Moved(delta Vec) Matrix {
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m[4], m[5] = m[4]+delta.X, m[5]+delta.Y
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return m
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}
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// ScaledXY scales everything around a given point by the scale factor in each axis respectively.
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func (m Matrix) ScaledXY(around Vec, scale Vec) Matrix {
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m[4], m[5] = m[4]-around.X, m[5]-around.Y
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m[0], m[2], m[4] = m[0]*scale.X, m[2]*scale.X, m[4]*scale.X
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m[1], m[3], m[5] = m[1]*scale.Y, m[3]*scale.Y, m[5]*scale.Y
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m[4], m[5] = m[4]+around.X, m[5]+around.Y
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return m
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}
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// Scaled scales everything around a given point by the scale factor.
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func (m Matrix) Scaled(around Vec, scale float64) Matrix {
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return m.ScaledXY(around, V(scale, scale))
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}
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// Rotated rotates everything around a given point by the given angle in radians.
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func (m Matrix) Rotated(around Vec, angle float64) Matrix {
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sint, cost := math.Sincos(angle)
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m[4], m[5] = m[4]-around.X, m[5]-around.Y
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m = m.Chained(Matrix{cost, sint, -sint, cost, 0, 0})
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m[4], m[5] = m[4]+around.X, m[5]+around.Y
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return m
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}
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// Chained adds another Matrix to this one. All tranformations by the next Matrix will be applied
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// after the transformations of this Matrix.
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func (m Matrix) Chained(next Matrix) Matrix {
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return Matrix{
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next[0]*m[0] + next[2]*m[1],
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next[1]*m[0] + next[3]*m[1],
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next[0]*m[2] + next[2]*m[3],
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next[1]*m[2] + next[3]*m[3],
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next[0]*m[4] + next[2]*m[5] + next[4],
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next[1]*m[4] + next[3]*m[5] + next[5],
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}
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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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//
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// Time complexity is O(1).
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func (m Matrix) Project(u Vec) Vec {
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return Vec{m[0]*u.X + m[2]*u.Y + m[4], m[1]*u.X + m[3]*u.Y + m[5]}
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}
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// Unproject does the inverse operation to Project.
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//
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// Time complexity is O(1).
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func (m Matrix) Unproject(u Vec) Vec {
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det := m[0]*m[3] - m[2]*m[1]
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return Vec{
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(m[3]*(u.X-m[4]) - m[2]*(u.Y-m[5])) / det,
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(-m[1]*(u.X-m[4]) + m[0]*(u.Y-m[5])) / det,
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}
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}
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