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