refacteur

engine/actor.go

@@ -2,6 +2,8 @@ package engine
 
 import (
 	"encoding/gob"
+
+	"drjosh.dev/gurgle/geom"
 )
 
 // Ensure Actor satisfies interfaces.
@@ -16,17 +18,17 @@ func init() {
 
 // Actor handles basic movement.
 type Actor struct {
-	CollisionDomain string // id of component to look for colliders inside of
+	CollisionDomain string    // id of component to look for colliders inside of
-	Pos, Size       Int3   // in voxels; multiply by game.VoxelScale for regular Euclidean space
+	Pos, Size       geom.Int3 // in voxels; multiply by game.VoxelScale for regular Euclidean space
 
-	rem  Float3
+	rem  geom.Float3
 	game *Game
 }
 
 // CollidesAt runs a collision test of the actor, supposing the actor is at a
 // given position (not necessarily a.Pos).
-func (a *Actor) CollidesAt(p Int3) bool {
+func (a *Actor) CollidesAt(p geom.Int3) bool {
-	bounds := Box{Min: p, Max: p.Add(a.Size)}
+	bounds := geom.Box{Min: p, Max: p.Add(a.Size)}
 	for c := range a.game.Query(a.CollisionDomain, ColliderType) {
 		if c.(Collider).CollidesWith(bounds) {
 			return true
@@ -46,7 +48,7 @@ func (a *Actor) MoveX(x float64, onCollide func()) {
 		return
 	}
 	a.rem.X -= float64(move)
-	sign := sign(move)
+	sign := geom.Sign(move)
 	for move != 0 {
 		a.Pos.X += sign
 		move -= sign
@@ -70,7 +72,7 @@ func (a *Actor) MoveY(y float64, onCollide func()) {
 		return
 	}
 	a.rem.Y -= float64(move)
-	sign := sign(move)
+	sign := geom.Sign(move)
 	for move != 0 {
 		a.Pos.Y += sign
 		move -= sign
@@ -94,7 +96,7 @@ func (a *Actor) MoveZ(z float64, onCollide func()) {
 		return
 	}
 	a.rem.Z -= float64(move)
-	sign := sign(move)
+	sign := geom.Sign(move)
 	for move != 0 {
 		a.Pos.Z += sign
 		move -= sign

engine/billboard.go

@@ -4,6 +4,7 @@ import (
 	"encoding/gob"
 	"image"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -37,6 +38,6 @@ func (b *Billboard) Draw(screen *ebiten.Image, opts *ebiten.DrawImageOptions) {
 func (b *Billboard) Scan() []interface{} { return []interface{}{&b.Src} }
 
 func (b *Billboard) Transform() (opts ebiten.DrawImageOptions) {
-	opts.GeoM.Translate(cfloat(b.Pos))
+	opts.GeoM.Translate(geom.CFloat(b.Pos))
 	return opts
 }

engine/camera.go

@@ -4,6 +4,7 @@ import (
 	"encoding/gob"
 	"image"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -36,7 +37,7 @@ type Camera struct {
 
 // PointAt points the camera at a particular centre point and zoom, but adjusts
 // for the bounds of the child component (if available).
-func (c *Camera) PointAt(centre Int3, zoom float64) {
+func (c *Camera) PointAt(centre geom.Int3, zoom float64) {
 	// Special sauce: if Child has a BoundingRect, make some adjustments
 	bnd, ok := c.Child.(Bounder)
 	if !ok {
@@ -60,7 +61,7 @@ func (c *Camera) PointAt(centre Int3, zoom float64) {
 
 	// If the configured centre puts the camera out of bounds, move it.
 	// Camera frame currently Rectangle{ centre ± (screen/(2*zoom)) }.
-	sw2, sh2 := cfloat(c.game.ScreenSize.Div(2))
+	sw2, sh2 := geom.CFloat(c.game.ScreenSize.Div(2))
 	swz, shz := int(sw2/zoom), int(sh2/zoom)
 	cent := c.game.Projection.Project(centre)
 	if cent.X-swz < br.Min.X {
@@ -89,9 +90,9 @@ func (c *Camera) Scan() []interface{} { return []interface{}{c.Child} }
 
 // Transform returns the camera transform.
 func (c *Camera) Transform() (opts ebiten.DrawImageOptions) {
-	opts.GeoM.Translate(cfloat(c.Centre.Mul(-1)))
+	opts.GeoM.Translate(geom.CFloat(c.Centre.Mul(-1)))
 	opts.GeoM.Scale(c.Zoom, c.Zoom)
 	opts.GeoM.Rotate(c.Rotation)
-	opts.GeoM.Translate(cfloat(c.game.ScreenSize.Div(2)))
+	opts.GeoM.Translate(geom.CFloat(c.game.ScreenSize.Div(2)))
 	return opts
 }

engine/game.go

@@ -13,6 +13,7 @@ import (
 	"sync"
 	"time"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -41,8 +42,8 @@ type Game struct {
 	Hidden
 	ScreenSize image.Point
 	Root       interface{} // typically a *Scene or SceneRef though
-	Projection IntProjection
+	Projection geom.IntProjection
-	VoxelScale Float3
+	VoxelScale geom.Float3
 
 	dbmu     sync.RWMutex
 	byID     map[string]Identifier              // Named components by ID
@@ -266,8 +267,8 @@ func postorderWalk(component, parent interface{}, visit func(component, parent i
 // builds the component databases and then calls Prepare on every Preparer.
 // LoadAndPrepare must be called before any calls to Component or Query.
 func (g *Game) LoadAndPrepare(assets fs.FS) error {
-	if g.VoxelScale == (Float3{}) {
+	if g.VoxelScale == (geom.Float3{}) {
-		g.VoxelScale = Float3{1, 1, 1}
+		g.VoxelScale = geom.Float3{1, 1, 1}
 	}
 
 	// Load all the Loaders.

engine/interface.go

@@ -5,6 +5,7 @@ import (
 	"io/fs"
 	"reflect"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -49,7 +50,7 @@ type Bounder interface {
 
 // Collider components have tangible form.
 type Collider interface {
-	CollidesWith(Box) bool
+	CollidesWith(geom.Box) bool
 }
 
 // Disabler components can be disabled.

engine/misc.go

@@ -45,102 +45,3 @@ type ZOrder int
 
 // DrawOrder returns z as a int with 0 bias.
 func (z ZOrder) DrawOrder() (int, int) { return int(z), 0 }
-
-// ---------- Some helpers for image.Point ----------
-
-// cmul performs componentwise multiplication of two image.Points.
-func cmul(p, q image.Point) image.Point {
-	return image.Point{p.X * q.X, p.Y * q.Y}
-}
-
-// cdiv performs componentwise division of two image.Points.
-func cdiv(p, q image.Point) image.Point {
-	return image.Point{p.X / q.X, p.Y / q.Y}
-}
-
-// cfloat returns the components of an image.Point as two floats.
-func cfloat(p image.Point) (x, y float64) {
-	return float64(p.X), float64(p.Y)
-}
-
-// dot returns the dot product of two image.Points.
-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 {
-	if polygon[0].In(rect) {
-		return true
-	}
-
-	// Check if any vertex of the rect is inside the polygon.
-	if polygonContains(polygon, rect.Min) {
-		return true
-	}
-
-	// Reduced Max (to the inclusive bound).
-	rmax := rect.Max.Sub(image.Pt(1, 1))
-
-	// Only remaining cases involve line intersection between the rect and poly
-	// having eliminated the possibility that one is entirely within another.
-
-	// Since rect is an axis-aligned rectangle, we only need vertical and
-	// horizontal line intersection tests.
-	// Walk each edge of polygon.
-	for i, p := range polygon {
-		q := polygon[(i+1)%len(polygon)]
-		// Pretend the edge is a rectangle. Exclude those that don't overlap.
-		if !rect.Overlaps(image.Rectangle{p, q}.Canon()) {
-			continue
-		}
-
-		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 t := (rect.Min.X - p.X) * d.Y; min <= t && t < max {
-				return true
-			}
-			// Test right side of rect
-			if t := (rmax.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 t := (rect.Min.Y - p.Y) * d.X; min <= t && t < max {
-				return true
-			}
-			// Test bottom side of rect
-			if t := (rmax.Y - p.Y) * d.X; min <= t && t < max {
-				return true
-			}
-		}
-	}
-	return false
-}

engine/parallax.go

@@ -4,6 +4,7 @@ import (
 	"encoding/gob"
 	"fmt"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -42,7 +43,7 @@ func (p *Parallax) Scan() []interface{} { return []interface{}{p.Child} }
 
 // Transform returns a GeoM translation of Factor * camera.Centre.
 func (p *Parallax) Transform() (opts ebiten.DrawImageOptions) {
-	x, y := cfloat(p.camera.Centre)
+	x, y := geom.CFloat(p.camera.Centre)
 	opts.GeoM.Translate(x*p.Factor, y*p.Factor)
 	return opts
 }

engine/prisms.go

@@ -5,6 +5,7 @@ import (
 	"fmt"
 	"image"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -35,19 +36,19 @@ type PrismMap struct {
 	Disabled
 	Hidden
 	Ersatz        bool
-	Map           map[Int3]*Prism // pos -> prism
+	Map           map[geom.Int3]*Prism // pos -> prism
-	DrawOrderBias image.Point     // dot with pos.XY() = bias value
+	DrawOrderBias image.Point          // dot with pos.XY() = bias value
-	DrawOffset    image.Point     // offset applies to whole map
+	DrawOffset    image.Point          // offset applies to whole map
-	PosToWorld    IntMatrix3x4    // p.pos -> world voxelspace
+	PosToWorld    geom.IntMatrix3x4    // p.pos -> world voxelspace
-	PrismSize     Int3            // in world voxelspace units
+	PrismSize     geom.Int3            // in world voxelspace units
-	PrismTop      []image.Point   // polygon vertices anticlockwise, Y means Z
+	PrismTop      []image.Point        // polygon vertices anticlockwise, Y means Z
 	Sheet         Sheet
 
 	game      *Game
-	pwinverse RatMatrix3
+	pwinverse geom.RatMatrix3
 }
 
-func (m *PrismMap) CollidesWith(b Box) bool {
+func (m *PrismMap) CollidesWith(b geom.Box) bool {
 	if m.Ersatz {
 		return false
 	}
@@ -65,10 +66,10 @@ func (m *PrismMap) CollidesWith(b Box) bool {
 	rb = rb.Canon() // inverse might flip the corners around...
 
 	// Check neighboring prisms too because there's a fencepost somewhere here
-	rb.Min = rb.Min.Sub(Int3{1, 1, 1})
+	rb.Min = rb.Min.Sub(geom.Int3{1, 1, 1})
-	rb.Max = rb.Max.Add(Int3{1, 1, 1})
+	rb.Max = rb.Max.Add(geom.Int3{1, 1, 1})
 
-	var pp Int3
+	var pp geom.Int3
 	for pp.Z = rb.Min.Z; pp.Z <= rb.Max.Z; pp.Z++ {
 		for pp.Y = rb.Min.Y; pp.Y <= rb.Max.Y; pp.Y++ {
 			for pp.X = rb.Min.X; pp.X <= rb.Max.X; pp.X++ {
@@ -78,13 +79,13 @@ func (m *PrismMap) CollidesWith(b Box) bool {
 				}
 				// Map it back to worldspace to get a bounding box for the prism
 				wp := m.PosToWorld.Apply(pp)
-				cb := Box{Min: wp, Max: wp.Add(m.PrismSize)}
+				cb := geom.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) {
+				if geom.PolygonRectOverlap(m.PrismTop, r) {
 					return true
 				}
 			}
@@ -102,7 +103,7 @@ func (m *PrismMap) CollidesWith(b Box) bool {
 			}
 			// Take into account the prism shape
 			r := b.XZ().Sub(wp.XZ())
-			if polygonRectOverlap(m.PrismTop, r) {
+			if geom.PolygonRectOverlap(m.PrismTop, r) {
 				return true
 			}
 		}
@@ -134,14 +135,14 @@ func (m *PrismMap) Scan() []interface{} {
 }
 
 func (m *PrismMap) Transform() (opts ebiten.DrawImageOptions) {
-	opts.GeoM.Translate(cfloat(m.DrawOffset))
+	opts.GeoM.Translate(geom.CFloat(m.DrawOffset))
 	return opts
 }
 
 type Prism struct {
 	Cell int
 
-	pos Int3
+	pos geom.Int3
 	m   *PrismMap
 }
 
@@ -151,11 +152,11 @@ func (p *Prism) Draw(screen *ebiten.Image, opts *ebiten.DrawImageOptions) {
 
 func (p *Prism) DrawOrder() (int, int) {
 	return p.m.PosToWorld.Apply(p.pos).Z,
-		dot(p.pos.XY(), p.m.DrawOrderBias)
+		geom.Dot(p.pos.XY(), p.m.DrawOrderBias)
 }
 
 func (p *Prism) Transform() (opts ebiten.DrawImageOptions) {
-	opts.GeoM.Translate(cfloat(
+	opts.GeoM.Translate(geom.CFloat(
 		p.m.game.Projection.Project(p.m.PosToWorld.Apply(p.pos)),
 	))
 	return opts

engine/sheet.go

@@ -3,6 +3,7 @@ package engine
 import (
 	"image"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -50,7 +51,7 @@ func (s *Sheet) Scan() []interface{} { return []interface{}{&s.Src} }
 
 // SubImage returns an *ebiten.Image corresponding to the given cell index.
 func (s *Sheet) SubImage(i int) *ebiten.Image {
-	p := cmul(image.Pt(i%s.w, i/s.w), s.CellSize)
+	p := geom.CMul(image.Pt(i%s.w, i/s.w), s.CellSize)
 	r := image.Rectangle{p, p.Add(s.CellSize)}
 	return s.Src.Image().SubImage(r).(*ebiten.Image)
 }

engine/solid.go

@@ -2,6 +2,8 @@ package engine
 
 import (
 	"encoding/gob"
+
+	"drjosh.dev/gurgle/geom"
 )
 
 var _ Collider = SolidRect{}
@@ -12,9 +14,9 @@ func init() {
 
 type SolidRect struct {
 	ID
-	Box
+	geom.Box
 }
 
-func (s SolidRect) CollidesWith(r Box) bool {
+func (s SolidRect) CollidesWith(r geom.Box) bool {
 	return s.Box.Overlaps(r)
 }

engine/sprite.go

@@ -4,6 +4,7 @@ import (
 	"encoding/gob"
 	"image"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -58,7 +59,7 @@ func (s *Sprite) SetAnim(a *Anim) {
 
 // Transform returns a translation by the DrawOffset and Actor.Pos projected
 func (s *Sprite) Transform() (opts ebiten.DrawImageOptions) {
-	opts.GeoM.Translate(cfloat(
+	opts.GeoM.Translate(geom.CFloat(
 		// 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...

engine/tiles.go

@@ -6,6 +6,7 @@ import (
 	"image"
 	"io/fs"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -47,15 +48,15 @@ type Tilemap struct {
 }
 
 // CollidesWith implements Collider.
-func (t *Tilemap) CollidesWith(b Box) bool {
+func (t *Tilemap) CollidesWith(b geom.Box) bool {
 	if t.Ersatz {
 		return false
 	}
 
 	// Probe the map at all tilespace coordinates overlapping the rect.
 	r := b.XY().Sub(t.Offset) // TODO: pretend tilemap is a plane in 3D?
-	min := cdiv(r.Min, t.Sheet.CellSize)
+	min := geom.CDiv(r.Min, t.Sheet.CellSize)
-	max := cdiv(r.Max.Sub(image.Pt(1, 1)), t.Sheet.CellSize) // NB: fencepost
+	max := geom.CDiv(r.Max.Sub(image.Pt(1, 1)), t.Sheet.CellSize) // NB: fencepost
 
 	for j := min.Y; j <= max.Y; j++ {
 		for i := min.X; i <= max.X; i++ {
@@ -74,10 +75,10 @@ func (t *Tilemap) Draw(screen *ebiten.Image, opts *ebiten.DrawImageOptions) {
 		if tile == nil {
 			continue
 		}
-		var geom ebiten.GeoM
+		var mat ebiten.GeoM
-		geom.Translate(cfloat(cmul(p, t.Sheet.CellSize)))
+		mat.Translate(geom.CFloat(geom.CMul(p, t.Sheet.CellSize)))
-		geom.Concat(og)
+		mat.Concat(og)
-		opts.GeoM = geom
+		opts.GeoM = mat
 
 		src := t.Sheet.SubImage(tile.Cell())
 		screen.DrawImage(src, opts)
@@ -111,24 +112,24 @@ func (t *Tilemap) Scan() []interface{} {
 
 // Transform returns a translation by t.Offset.
 func (t *Tilemap) Transform() (opts ebiten.DrawImageOptions) {
-	opts.GeoM.Translate(cfloat(t.Offset))
+	opts.GeoM.Translate(geom.CFloat(t.Offset))
 	return opts
 }
 
 // TileAt returns the tile present at the given world coordinate.
 func (t *Tilemap) TileAt(wc image.Point) Tile {
-	return t.Map[cdiv(wc.Sub(t.Offset), t.Sheet.CellSize)]
+	return t.Map[geom.CDiv(wc.Sub(t.Offset), t.Sheet.CellSize)]
 }
 
 // SetTileAt sets the tile at the given world coordinate.
 func (t *Tilemap) SetTileAt(wc image.Point, tile Tile) {
-	t.Map[cdiv(wc.Sub(t.Offset), t.Sheet.CellSize)] = tile
+	t.Map[geom.CDiv(wc.Sub(t.Offset), t.Sheet.CellSize)] = tile
 }
 
 // TileBounds returns a rectangle describing the tile boundary for the tile
 // at the given world coordinate.
 func (t *Tilemap) TileBounds(wc image.Point) image.Rectangle {
-	p := cmul(cdiv(wc.Sub(t.Offset), t.Sheet.CellSize), t.Sheet.CellSize).Add(t.Offset)
+	p := geom.CMul(geom.CDiv(wc.Sub(t.Offset), t.Sheet.CellSize), t.Sheet.CellSize).Add(t.Offset)
 	return image.Rectangle{p, p.Add(t.Sheet.CellSize)}
 }
 

engine/walls.go

@@ -3,6 +3,7 @@ package engine
 import (
 	"image"
 
+	"drjosh.dev/gurgle/geom"
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
@@ -39,15 +40,15 @@ type Wall struct {
 }
 
 // CollidesWith implements a tilerange collosion check, similar to Tilemap.
-func (w *Wall) CollidesWith(b Box) bool {
+func (w *Wall) CollidesWith(b geom.Box) bool {
 	if w.Ersatz {
 		return false
 	}
 
 	// Probe the map at all tilespace coordinates overlapping the rect.
 	r := b.XY().Sub(w.Offset)
-	min := cdiv(r.Min, w.UnitSize)
+	min := geom.CDiv(r.Min, w.UnitSize)
-	max := cdiv(r.Max.Sub(image.Pt(1, 1)), w.UnitSize) // NB: fencepost
+	max := geom.CDiv(r.Max.Sub(image.Pt(1, 1)), w.UnitSize) // NB: fencepost
 
 	for j := min.Y; j <= max.Y; j++ {
 		for i := min.X; i <= max.X; i++ {
@@ -81,7 +82,7 @@ func (w *Wall) Prepare(*Game) error {
 
 // Transform returns a GeoM translation by Offset.
 func (w *Wall) Transform() (opts ebiten.DrawImageOptions) {
-	opts.GeoM.Translate(cfloat(w.Offset))
+	opts.GeoM.Translate(geom.CFloat(w.Offset))
 	return opts
 }
 
@@ -106,8 +107,8 @@ func (u *WallUnit) Draw(screen *ebiten.Image, opts *ebiten.DrawImageOptions) {
 func (u *WallUnit) Scan() []interface{} { return []interface{}{u.Tile} }
 
 func (u *WallUnit) Transform() (opts ebiten.DrawImageOptions) {
-	opts.GeoM.Translate(cfloat(
+	opts.GeoM.Translate(geom.CFloat(
-		cmul(u.pos, u.wall.UnitSize).Add(u.wall.UnitOffset),
+		geom.CMul(u.pos, u.wall.UnitSize).Add(u.wall.UnitOffset),
 	))
 	return opts
 }

geom/box.go

@@ -1,4 +1,4 @@
-package engine
+package geom
 
 import "image"
 

geom/matrix.go

@@ -1,4 +1,4 @@
-package engine
+package geom
 
 import (
 	"errors"

geom/misc.go

@@ -0,0 +1,25 @@
+package geom
+
+import "image"
+
+// ---------- Some helpers for image.Point ----------
+
+// CMul performs componentwise multiplication of two image.Points.
+func CMul(p, q image.Point) image.Point {
+	return image.Point{p.X * q.X, p.Y * q.Y}
+}
+
+// CDiv performs componentwise division of two image.Points.
+func CDiv(p, q image.Point) image.Point {
+	return image.Point{p.X / q.X, p.Y / q.Y}
+}
+
+// CFloat returns the components of an image.Point as two floats.
+func CFloat(p image.Point) (x, y float64) {
+	return float64(p.X), float64(p.Y)
+}
+
+// Dot returns the Dot product of two image.Points.
+func Dot(p, q image.Point) int {
+	return p.X*q.X + p.Y*q.Y
+}

geom/point.go

@@ -1,4 +1,4 @@
-package engine
+package geom
 
 import (
 	"fmt"
@@ -73,7 +73,7 @@ func (p Int3) Coord() (x, y, z int) {
 
 // Sign returns a sign vector.
 func (p Int3) Sign() Int3 {
-	return Int3{sign(p.X), sign(p.Y), sign(p.Z)}
+	return Int3{Sign(p.X), Sign(p.Y), Sign(p.Z)}
 }
 
 // Dot returns the dot product of the two vectors.
@@ -81,7 +81,8 @@ func (p Int3) Dot(q Int3) int {
 	return p.X*q.X + p.Y*q.Y + p.Z*q.Z
 }
 
-func sign(m int) int {
+// Sign returns the sign of the int (-1, 0, or 1).
+func Sign(m int) int {
 	if m == 0 {
 		return 0
 	}
@@ -91,7 +92,8 @@ func sign(m int) int {
 	return 1
 }
 
-func signf(m float64) float64 {
+// FSign returns the sign of the float64 (-1, 0, or 1).
+func FSign(m float64) float64 {
 	if m == 0 {
 		return 0
 	}
@@ -153,7 +155,7 @@ func (p Float3) Coord() (x, y, z float64) {
 
 // Sign returns a sign vector.
 func (p Float3) Sign() Float3 {
-	return Float3{signf(p.X), signf(p.Y), signf(p.Z)}
+	return Float3{FSign(p.X), FSign(p.Y), FSign(p.Z)}
 }
 
 // Dot returns the dot product of the two vectors.

geom/polygon.go

@@ -0,0 +1,80 @@
+package geom
+
+import "image"
+
+// 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 {
+	if polygon[0].In(rect) {
+		return true
+	}
+
+	// Check if any vertex of the rect is inside the polygon.
+	if PolygonContains(polygon, rect.Min) {
+		return true
+	}
+
+	// Reduced Max (to the inclusive bound).
+	rmax := rect.Max.Sub(image.Pt(1, 1))
+
+	// Only remaining cases involve line intersection between the rect and poly
+	// having eliminated the possibility that one is entirely within another.
+
+	// Since rect is an axis-aligned rectangle, we only need vertical and
+	// horizontal line intersection tests.
+	// Walk each edge of polygon.
+	for i, p := range polygon {
+		q := polygon[(i+1)%len(polygon)]
+		// Pretend the edge is a rectangle. Exclude those that don't overlap.
+		if !rect.Overlaps(image.Rectangle{p, q}.Canon()) {
+			continue
+		}
+
+		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 t := (rect.Min.X - p.X) * d.Y; min <= t && t < max {
+				return true
+			}
+			// Test right side of rect
+			if t := (rmax.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 t := (rect.Min.Y - p.Y) * d.X; min <= t && t < max {
+				return true
+			}
+			// Test bottom side of rect
+			if t := (rmax.Y - p.Y) * d.X; min <= t && t < max {
+				return true
+			}
+		}
+	}
+	return false
+}

geom/polygon_test.go

@@ -0,0 +1,28 @@
+package geom
+
+import (
+	"image"
+	"testing"
+)
+
+func TestPolygonContains(t *testing.T) {
+	square5 := []image.Point{
+		{X: 0, Y: 0},
+		{X: 5, Y: 0},
+		{X: 5, Y: 5},
+		{X: 0, Y: 5},
+	}
+	tests := []struct {
+		polygon []image.Point
+		point   image.Point
+		want    bool
+	}{
+		{square5, image.Pt(2, 3), true},
+	}
+
+	for _, test := range tests {
+		if got, want := PolygonContains(test.polygon, test.point), test.want; got != want {
+			t.Errorf("polygonContains(%v, %v) = %v, want %v", test.polygon, test.point, got, want)
+		}
+	}
+}

geom/projection.go

@@ -1,4 +1,4 @@
-package engine
+package geom
 
 import "image"
 

geom/rational.go

@@ -1,4 +1,4 @@
-package engine
+package geom
 
 import "strconv"