119 lines
2.9 KiB
Go
119 lines
2.9 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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// 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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// 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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// Box describes an axis-aligned rectangular prism.
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type Box struct {
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Min, Max Point3
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}
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// String returns a string representation of b like "(3,4,5)-(6,5,8)".
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func (b Box) String() string {
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return b.Min.String() + "-" + b.Max.String()
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}
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// Empty reports whether the box contains no points.
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func (b Box) Empty() bool {
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return b.Min.X >= b.Max.X || b.Min.Y >= b.Max.Y || b.Min.Z >= b.Max.Z
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}
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// Eq reports whether b and c contain the same set of points. All empty boxes
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// are considered equal.
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func (b Box) Eq(c Box) bool {
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return b == c || b.Empty() && c.Empty()
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}
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// Overlaps reports whether b and c have non-empty intersection.
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func (b Box) Overlaps(c Box) bool {
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return !b.Empty() && !c.Empty() &&
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b.Min.X < c.Max.X && c.Min.X < b.Max.X &&
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b.Min.Y < c.Max.Y && c.Min.Y < b.Max.Y &&
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b.Min.Z < c.Max.Z && c.Min.Z < b.Max.Z
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}
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// Size returns b's width, height, and depth.
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func (b Box) Size() Point3 {
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return b.Max.Sub(b.Min)
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}
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