WIP: committing some ideas

engine/matrix.go

@@ -0,0 +1,60 @@
+package engine
+
+import "image"
+
+// IntMatrix3 implements a 3x3 integer matrix.
+type IntMatrix3 [3][3]int
+
+// Apply applies the matrix to a vector to obtain a transformed vector.
+func (a IntMatrix3) Apply(v Point3) Point3 {
+	return Point3{
+		X: v.X*a[0][0] + v.Y*a[0][1] + v.Z*a[0][2],
+		Y: v.X*a[1][0] + v.Y*a[1][1] + v.Z*a[1][2],
+		Z: v.X*a[2][0] + v.Y*a[2][1] + v.Z*a[2][2],
+	}
+}
+
+// Concat returns the matrix equivalent to applying matrix a and then b.
+func (a IntMatrix3) Concat(b IntMatrix3) IntMatrix3 {
+	return IntMatrix3{
+		[3]int{
+			a[0][0]*b[0][0] + a[0][1]*b[1][0] + a[0][2]*b[2][0],
+			a[0][0]*b[0][1] + a[0][1]*b[1][1] + a[0][2]*b[2][1],
+			a[0][0]*b[0][2] + a[0][1]*b[1][2] + a[0][2]*b[2][2],
+		},
+		[3]int{
+			a[1][0]*b[0][0] + a[1][1]*b[1][0] + a[1][2]*b[2][0],
+			a[1][0]*b[0][1] + a[1][1]*b[1][1] + a[1][2]*b[2][1],
+			a[1][0]*b[0][2] + a[1][1]*b[1][2] + a[1][2]*b[2][2],
+		},
+		[3]int{
+			a[2][0]*b[0][0] + a[2][1]*b[1][0] + a[2][2]*b[2][0],
+			a[2][0]*b[0][1] + a[2][1]*b[1][1] + a[2][2]*b[2][1],
+			a[2][0]*b[0][2] + a[2][1]*b[1][2] + a[2][2]*b[2][2],
+		},
+	}
+}
+
+// IntMatrix3x4 implements a 3 row, 4 column integer matrix, capable of
+//describing any integer affine transformation.
+type IntMatrix3x4 [3][4]int
+
+// Apply applies the matrix to a vector to obtain a transformed vector.
+func (a IntMatrix3x4) Apply(v Point3) Point3 {
+	return Point3{
+		X: v.X*a[0][0] + v.Y*a[0][1] + v.Z*a[0][2] + a[0][3],
+		Y: v.X*a[1][0] + v.Y*a[1][1] + v.Z*a[1][2] + a[1][3],
+		Z: v.X*a[2][0] + v.Y*a[2][1] + v.Z*a[2][2] + a[2][3],
+	}
+}
+
+// IntMatrix2x3 implements a 2 row, 3 column matrix (as two Point3 row vectors).
+type IntMatrix2x3 [2]Point3
+
+// Apply applies the matrix to a vector to obtain a transformed vector.
+func (a IntMatrix2x3) Apply(v Point3) image.Point {
+	return image.Point{
+		X: v.Dot(a[0]),
+		Y: v.Dot(a[1]),
+	}
+}

engine/point.go

@@ -70,6 +70,11 @@ func (p Point3) Sign() Point3 {
 	return Point3{sign(p.X), sign(p.Y), sign(p.Z)}
 }
 
+// Dot returns the dot product of the two vectors.
+func (p Point3) Dot(q Point3) int {
+	return p.X*q.X + p.Y*q.Y + p.Z*q.Z
+}
+
 func sign(m int) int {
 	if m == 0 {
 		return 0

engine/prisms.go

@@ -36,13 +36,16 @@ type PrismMap struct {
 	Map           map[Point3]*Prism // pos -> prism
 	DrawOrderBias image.Point       // dot with pos.XY() = bias value
 	DrawOffset    image.Point       // offset applies to whole map
-	DrawZStride   image.Point // draw offset for each pos unit in Z
+	PosToDraw     IntMatrix2x3      // p.pos -> drawspace (before offset and camera and ...)
-	PrismSize     Point3      // (prismsize cmul pos) = world position
+	PosToWorld    IntMatrix3x4      // p.pos -> worldspace
+	PrismSize     Point3            // in worldspace
 	Sheet         Sheet
 }
 
 func (m *PrismMap) CollidesWith(b Box) bool {
-	// TODO
+	// Back corner of a prism p is:
+	// m.PrismPos.Apply(p.pos)
+
 	return false
 }
 
@@ -71,14 +74,13 @@ func (p *Prism) Draw(screen *ebiten.Image, opts *ebiten.DrawImageOptions) {
 }
 
 func (p *Prism) DrawOrder() (int, int) {
-	return p.pos.Z * p.pm.PrismSize.Z,
+	return p.pm.PosToWorld.Apply(p.pos).Z,
 		dot(p.pos.XY(), p.pm.DrawOrderBias)
 }
 
 func (p *Prism) Transform(pt Transform) (tf Transform) {
 	tf.Opts.GeoM.Translate(cfloat(
-		cmul(p.pos.XY(), p.pm.PrismSize.XY()).
+		p.pm.PosToDraw.Apply(p.pos),
-			Add(p.pm.DrawZStride.Mul(p.pos.Z)),
 	))
 	return tf.Concat(pt)
 }

engine/projection.go

@@ -6,11 +6,11 @@ var (
 	CavalierProjection = ParallelProjection{1, 1}
 
 	// Axonometric projections
-	DimetricProjection  = ParallelProjection{0, 0.5}
 	ElevationProjection = ParallelProjection{0, 0}
+	DimetricProjection  = ParallelProjection{0, 0.5}
+	HexPrismProjection  = ParallelProjection{0, 0.577350269189626} // 1 ÷ √3
 	IsometricProjection = ParallelProjection{0, 0.707106781186548} // 1 ÷ √2
 	TrimetricProjection = ParallelProjection{0, 1}
-	HexPrismProjection  = ParallelProjection{0, 0.816496580927726} // √2 ÷ √3
 )
 
 type ParallelProjection struct {