π.Project -> geom.Project(π,

engine/billboard.go

@@ -83,7 +83,7 @@ func (b *Billboard) String() string {
 // Transform returns a translation by the projected position.
 func (b *Billboard) Transform() (opts ebiten.DrawImageOptions) {
 	opts.GeoM.Translate(geom.CFloat(
-		b.game.Projection.Project(b.Pos),
+		geom.Project(b.game.Projection, b.Pos),
 	))
 	return opts
 }

engine/camera.go

@@ -41,7 +41,7 @@ func (c *Camera) PointAt(centre geom.Int3, zoom float64) {
 	// Special sauce: if Child has a BoundingRect, make some adjustments
 	bnd, ok := c.Child.(BoundingRecter)
 	if !ok {
-		c.Centre = c.game.Projection.Project(centre)
+		c.Centre = geom.Project(c.game.Projection, centre)
 		c.Zoom = zoom
 		return
 	}
@@ -63,7 +63,7 @@ func (c *Camera) PointAt(centre geom.Int3, zoom float64) {
 	// Camera frame currently Rectangle{ centre ± (screen/(2*zoom)) }.
 	sw2, sh2 := geom.CFloat(c.game.ScreenSize.Div(2))
 	swz, shz := int(sw2/zoom), int(sh2/zoom)
-	cent := c.game.Projection.Project(centre)
+	cent := geom.Project(c.game.Projection, centre)
 	if cent.X-swz < br.Min.X {
 		cent.X = br.Min.X + swz
 	}

engine/prisms.go

@@ -212,7 +212,7 @@ func (p *Prism) String() string {
 // Transform returns a translation by the projected position.
 func (p *Prism) Transform() (opts ebiten.DrawImageOptions) {
 	opts.GeoM.Translate(geom.CFloat(
-		p.m.game.Projection.Project(p.pos),
+		geom.Project(p.m.game.Projection, p.pos),
 	))
 	return opts
 }

engine/sprite.go

@@ -67,7 +67,8 @@ func (s *Sprite) Transform() (opts ebiten.DrawImageOptions) {
 		// Reaching into Actor for a reference to Game so I don't have to
 		// implement Prepare in this file, but writing this long comment
 		// providing exposition...
-		s.Actor.game.Projection.Project(s.Actor.Pos).Add(s.DrawOffset),
+		geom.Project(s.Actor.game.Projection, s.Actor.Pos).
+			Add(s.DrawOffset),
 	))
 	return opts
 }

geom/box.go

@@ -80,7 +80,7 @@ func (b Box) BoundingRect(π Projector) image.Rectangle {
 // Back returns an image.Rectangle representing the back of the box, using
 // the given projection π.
 func (b Box) Back(π Projector) image.Rectangle {
-	p := π.Project(Int3{0, 0, b.Min.Z})
+	p := π.Project(b.Min.Z)
 	return image.Rectangle{
 		Min: b.Min.XY().Add(p),
 		Max: b.Max.XY().Add(p),
@@ -90,7 +90,7 @@ func (b Box) Back(π Projector) image.Rectangle {
 // Front returns an image.Rectangle representing the front of the box, using
 // the given projection π.
 func (b Box) Front(π Projector) image.Rectangle {
-	p := π.Project(Int3{0, 0, b.Max.Z})
+	p := π.Project(b.Max.Z)
 	return image.Rectangle{
 		Min: b.Min.XY().Add(p),
 		Max: b.Max.XY().Add(p),

geom/projection.go

@@ -7,8 +7,13 @@ type Projector interface {
 	// Sign returns a {-1, 0, 1}-valued 2D vector pointing in the direction that
 	// positive Z values are projected to.
 	Sign() image.Point
-	// Project projects a 3D point into 2D.
-	Project(Int3) image.Point
+	// Project projects a Z coordinate into 2D offset.
+	Project(int) image.Point
+}
+
+// Project is shorthand for π.Project(p.Z).Add(p.XY()).
+func Project(π Projector, p Int3) image.Point {
+	return π.Project(p.Z).Add(p.XY())
 }
 
 // Projection uses floats to define a projection.
@@ -18,26 +23,24 @@ func (π Projection) Sign() (s image.Point) {
 	return image.Pt(int(FSign(π.X)), int(FSign(π.Y)))
 }
 
-// Project performs a parallel projection of a 3D coordiante into 2D.
-// x projects to (x + z*π.X), and y to (y + z*π.Y)
-func (π Projection) Project(p Int3) image.Point {
+// Project returns (z*π.X, z*π.Y).
+func (π Projection) Project(z int) image.Point {
 	return image.Pt(
-		p.X+int(π.X*float64(p.Z)),
-		p.Y+int(π.Y*float64(p.Z)),
+		int(π.X*float64(z)),
+		int(π.Y*float64(z)),
 	)
 }
 
 // IntProjection holds an integer projection definition.
 // It is designed for projecting Z onto X and Y with integer fractions as would
-// be used in e.g. a diametric projection (IntProjection{X:0, Y:-2}).
+// be used in e.g. a diametric projection (IntProjection{X:0, Y:2}).
 type IntProjection image.Point
 
 func (π IntProjection) Sign() image.Point { return image.Point(π) }
 
-// Project performs an integer parallel 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 (π IntProjection) Project(p Int3) image.Point {
+// Project returns (z/π.X, z/π.Y), unless π.X or π.Y are 0, in which case that
+// component is zero
+func (π IntProjection) Project(z int) image.Point {
 	/*
 		Dividing is used because there's little reason for an isometric
 		projection in a game to exaggerate the Z position.
@@ -45,12 +48,12 @@ func (π IntProjection) Project(p Int3) image.Point {
 		Integers are used to preserve "pixel perfect" calculation in case you
 		are making the next Celeste.
 	*/
-	q := p.XY()
+	var q image.Point
 	if π.X != 0 {
-		q.X += p.Z / π.X
+		q.X = z / π.X
 	}
 	if π.Y != 0 {
-		q.Y += p.Z / π.Y
+		q.Y = z / π.Y
 	}
 	return q
 }