110 lines
2.5 KiB
Go
110 lines
2.5 KiB
Go
package engine
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import (
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"image"
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"strconv"
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)
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// Point3 is a an element of int^3.
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type Point3 struct {
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X, Y, Z int
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}
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// Pt3(x, y, z) is shorthand for Point3{x, y, z}.
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func Pt3(x, y, z int) Point3 {
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return Point3{x, y, z}
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}
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// String returns a string representation of p like "(3,4,5)".
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func (p Point3) String() string {
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return "(" + strconv.Itoa(p.X) + "," + strconv.Itoa(p.Y) + "," + strconv.Itoa(p.Z) + ")"
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}
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// XY applies the Z-forgetting projection. (It returns just X and Y.)
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func (p Point3) XY() image.Point {
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return image.Point{p.X, p.Y}
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}
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// Add performs vector addition.
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func (p Point3) Add(q Point3) Point3 {
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return Point3{p.X + q.X, p.Y + q.Y, p.Z + q.Z}
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}
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// Sub performs vector subtraction.
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func (p Point3) Sub(q Point3) Point3 {
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return p.Add(q.Neg())
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}
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// CMul performs componentwise multiplication.
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func (p Point3) CMul(q Point3) Point3 {
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return Point3{p.X * q.X, p.Y * q.Y, p.Z * q.Z}
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}
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// Mul performs scalar multiplication.
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func (p Point3) Mul(k int) Point3 {
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return Point3{p.X * k, p.Y * k, p.Z * k}
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}
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// CDiv performs componentwise division.
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func (p Point3) CDiv(q Point3) Point3 {
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return Point3{p.X / q.X, p.Y / q.Y, p.Z / q.Z}
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}
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// Div performs scalar division by k.
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func (p Point3) Div(k int) Point3 {
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return Point3{p.X / k, p.Y / k, p.Z / k}
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}
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// Neg returns the vector pointing in the opposite direction.
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func (p Point3) Neg() Point3 {
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return Point3{-p.X, -p.Y, -p.Z}
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}
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// Coord returns the components of the vector.
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func (p Point3) Coord() (x, y, z int) {
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return p.X, p.Y, p.Z
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}
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// Sign returns a sign vector.
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func (p Point3) Sign() Point3 {
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return Point3{sign(p.X), sign(p.Y), sign(p.Z)}
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}
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// Dot returns the dot product of the two vectors.
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func (p Point3) Dot(q Point3) int {
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return p.X*q.X + p.Y*q.Y + p.Z*q.Z
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}
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func sign(m int) int {
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if m == 0 {
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return 0
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}
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if m < 0 {
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return -1
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}
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return 1
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}
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// IsoProject performs isometric projection of a 3D coordinate into 2D.
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//
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// If π.X = 0, the x returned is p.X; similarly for π.Y and y.
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// Otherwise, x projects to x + z/π.X and y projects to y + z/π.Y.
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func (p Point3) IsoProject(π image.Point) image.Point {
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/*
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I'm using the π character because I'm a maths wanker.
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Dividing is used because there's little reason for an isometric
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projection in a game to exaggerate the Z position.
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Integers are used to preserve that "pixel perfect" calculation in case
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you are making the next Celeste.
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*/
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q := image.Point{p.X, p.Y}
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if π.X != 0 {
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q.X += p.Z / π.X
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}
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if π.Y != 0 {
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q.Y += p.Z / π.Y
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}
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return q
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}
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