prism collism

engine/box.go

@@ -93,3 +93,11 @@ func (b Box) XY() image.Rectangle {
 		Max: b.Max.XY(),
 	}
 }
+
+// XZ returns the image.Rectangle representing the box if we forgot about Y.
+func (b Box) XZ() image.Rectangle {
+	return image.Rectangle{
+		Min: b.Min.XZ(),
+		Max: b.Max.XZ(),
+	}
+}

engine/misc.go

@@ -1,6 +1,8 @@
 package engine
 
-import "image"
+import (
+	"image"
+)
 
 // ID implements Identifier directly (as a string value).
 type ID string
@@ -65,3 +67,97 @@ func cfloat(p image.Point) (x, y float64) {
 func dot(p, q image.Point) int {
 	return p.X*q.X + p.Y*q.Y
 }
+
+// polygonContains reports if a polygon contains a point
+func polygonContains(polygon []image.Point, p image.Point) bool {
+	for i, p1 := range polygon {
+		p2 := polygon[(i+1)%len(polygon)]
+		// ∆(p p1 p2) should have positive signed area
+		p1, p2 = p1.Sub(p), p2.Sub(p)
+		if p2.X*p1.Y-p1.X*p2.Y < 0 {
+			return false
+		}
+	}
+	return true
+}
+
+// polygonRectOverlap reports if a polygon overlaps a rectangle.
+func polygonRectOverlap(polygon []image.Point, rect image.Rectangle) bool {
+	// There's a good chance a vertex from one thing is inside the other...
+
+	// Check if any vertex of the polygon is inside the rect.
+	for _, p := range polygon {
+		if p.In(rect) {
+			return true
+		}
+	}
+
+	// Reduce Max to the inclusive bound.
+	rect.Max = rect.Max.Sub(image.Pt(1, 1))
+
+	// Check if any vertex of the rect is inside the polygon.
+	if polygonContains(polygon, rect.Min) {
+		return true
+	}
+	if polygonContains(polygon, rect.Max) {
+		return true
+	}
+	if polygonContains(polygon, image.Pt(rect.Min.X, rect.Max.Y)) {
+		return true
+	}
+	if polygonContains(polygon, image.Pt(rect.Max.X, rect.Min.Y)) {
+		return true
+	}
+
+	// Only remaining cases involve line intersection between the rect and poly.
+
+	// Since rect is an axis-aligned rectangle, we only need vertical and
+	// horizontal line intersection tests.
+	// Walk each edge of polygon. Only a point and the ∆x, ∆y are needed.
+	for i, p := range polygon {
+		q := polygon[(i+1)%len(polygon)]
+		d := q.Sub(p)
+		// If the polygon edge is not vertical, test left and right sides
+		if d.X != 0 {
+			if d.X < 0 {
+				d = d.Mul(-1)
+			}
+			min := (rect.Min.Y - p.Y) * d.X
+			max := (rect.Max.Y - p.Y) * d.X
+			// Test left side of rect
+			if (rect.Min.X >= p.X || rect.Min.X >= q.X) && (rect.Min.X <= p.X || rect.Min.X <= q.X) {
+				if t := (rect.Min.X - p.X) * d.Y; min <= t && t <= max {
+					return true
+				}
+			}
+			// Test right side of rect
+			if (rect.Max.X >= p.X || rect.Max.X >= q.X) && (rect.Max.X <= p.X || rect.Max.X <= q.X) {
+				if t := (rect.Max.X - p.X) * d.Y; min <= t && t <= max {
+					return true
+				}
+			}
+		}
+		// If the polygon edge is not horizontal, test the top and bottom sides
+		if d.Y != 0 {
+			if d.Y < 0 {
+				d = d.Mul(-1)
+			}
+			min := (rect.Min.X - p.X) * d.Y
+			max := (rect.Max.X - p.X) * d.Y
+			// Test top side of rect
+			if (rect.Min.Y >= p.Y && rect.Min.Y >= q.Y) && (rect.Min.Y <= p.Y && rect.Min.Y <= q.Y) {
+				if t := (rect.Min.Y - p.Y) * d.X; min <= t && t <= max {
+					return true
+				}
+			}
+
+			// Test bottom side of rect
+			if (rect.Max.Y >= p.Y && rect.Max.Y >= q.Y) && (rect.Max.Y <= p.Y && rect.Max.Y <= q.Y) {
+				if t := (rect.Max.Y - p.Y) * d.X; min <= t && t <= max {
+					return true
+				}
+			}
+		}
+	}
+	return false
+}

engine/point.go

@@ -23,7 +23,12 @@ func (p Int3) String() string {
 
 // XY applies the Z-forgetting projection. (It returns just X and Y.)
 func (p Int3) XY() image.Point {
-	return image.Point{p.X, p.Y}
+	return image.Point{X: p.X, Y: p.Y}
+}
+
+// XZ applies the Y-forgetting projection. (It returns just X and Z (as Y).)
+func (p Int3) XZ() image.Point {
+	return image.Point{X: p.X, Y: p.Z}
 }
 
 // Add performs vector addition.

engine/prisms.go

@@ -40,6 +40,7 @@ type PrismMap struct {
 	DrawOffset    image.Point     // offset applies to whole map
 	PosToWorld    IntMatrix3x4    // p.pos -> world voxelspace
 	PrismSize     Int3            // in world voxelspace units
+	PrismTop      []image.Point   // polygon vertices anticlockwise, Y means Z
 	Sheet         Sheet
 
 	game      *Game
@@ -50,6 +51,7 @@ func (m *PrismMap) CollidesWith(b Box) bool {
 	if m.Ersatz {
 		return false
 	}
+
 	// To find the prisms need to test, we need to invert PosToWorld.
 
 	// Step 1: subtract whatever the translation component of PosToWorld is,
@@ -80,11 +82,31 @@ func (m *PrismMap) CollidesWith(b Box) bool {
 				if !b.Overlaps(cb) {
 					continue
 				}
-				// TODO: take into account the prism shape
+				// Take into account the prism shape
+				r := b.XZ().Sub(wp.XZ())
+				if polygonRectOverlap(m.PrismTop, r) {
 					return true
 				}
 			}
 		}
+	}
+
+	/*
+		// Here's the test-every-prism approach
+		for pos := range m.Map {
+			// Map it back to worldspace to get a bounding box for the prism
+			wp := m.PosToWorld.Apply(pos)
+			cb := Box{Min: wp, Max: wp.Add(m.PrismSize)}
+			if !b.Overlaps(cb) {
+				continue
+			}
+			// Take into account the prism shape
+			r := b.XZ().Sub(wp.XZ())
+			if polygonRectOverlap(m.PrismTop, r) {
+				return true
+			}
+		}
+	*/
 	return false
 }
 

main.go

@@ -121,6 +121,14 @@ func level1() *engine.Scene {
 					2: [4]int{8, 0, 16, 0},
 				},
 				PrismSize: engine.Int3{X: 32, Y: 16, Z: 16},
+				PrismTop: []image.Point{
+					{X: 8, Y: 0},
+					{X: 0, Y: 8},
+					{X: 8, Y: 16},
+					{X: 23, Y: 16},
+					{X: 31, Y: 8},
+					{X: 23, Y: 0},
+				},
 				Sheet: engine.Sheet{
 					CellSize: image.Pt(32, 32),
 					Src:      engine.ImageRef{Path: "assets/hexprism32.png"},