Point is now its own struct.

- Removed dependency on image package.
Added more methods to manipulate point.

point.go

@@ -1,19 +1,118 @@
 package geom
 
 import (
-	_image "image"
+	"fmt"
-	"strconv"
 )
 
-// Point is exposing the standard library image.Point in the geom package.
+// ZeroPt represents the coordinate (0, 0)
-type Point _image.Point
+var ZeroPt = Point{0, 0}
+
+// OnePt represents the coordinate (1, 1)
+var OnePt = Point{1, 1}
+
+// North represents the coordinate next to the ZeroPt (Y == -1)
+var North = Point{0, -1}
+
+// East represents the coordinate next to the ZeroPt (X == 1)
+var East = Point{1, 0}
+
+// South represents the coordinate next to the ZeroPt (Y == 1)
+var South = Point{0, 1}
+
+// West represents the coordinate next to the ZeroPt (X == -1)
+var West = Point{-1, 0}
+
+// Point represents a 2-dimensional point.
+type Point struct {
+	X, Y int
+}
 
 // Pt is a shorthand function to create a point.
 func Pt(x, y int) Point {
 	return Point{x, y}
 }
 
-// String formats the point p as a string.
+// NewPt is a short function to create a point and return a pointer to it.
-func (p Point) String() string {
+func NewPt(x, y int) *Point {
-	return "(" + strconv.Itoa(p.X) + "," + strconv.Itoa(p.Y) + ")"
+	return &Point{x, y}
+}
+
+// Abs returns a point the absolute values of X and Y.
+func (p Point) Abs() Point {
+	return Pt(AbsInt(p.X), AbsInt(p.Y))
+}
+
+// Add returns the sum of p and q.
+func (p Point) Add(q Point) Point {
+	return p.Add2D(q.X, q.Y)
+}
+
+// Add2D adds x and y to X and Y of point p and returns the sum.
+func (p Point) Add2D(x, y int) Point {
+	return Pt(p.X+x, p.Y+y)
+}
+
+// Less returns true if q is above (Y is smaller) or left (X is smaller) than p. Otherwise returns false.
+func (p Point) Less(q Point) bool {
+	if p.Y == q.Y {
+		return p.X < q.X
+	}
+	return p.Y < q.Y
+}
+
+// DistInt returns the integer distance between the points p and q.
+func (p Point) DistInt(q Point) int {
+	return SubAbsInt(p.X, q.X) + SubAbsInt(p.Y, q.Y)
+}
+
+// Mul multiplier the X and Y values of point p with t and returns the result.
+func (p Point) Mul(t int) Point {
+	return Pt(p.X*t, p.Y*t)
+}
+
+// Norm returns the point with both X and Y normalized.
+func (p Point) Norm() Point {
+	return Pt(NormInt(p.X), NormInt(p.Y))
+}
+
+// String returns a string representation of point p "X, Y".
+func (p Point) String() string {
+	return fmt.Sprintf("%d, %d", p.X, p.Y)
+}
+
+// StringBrackets formats the point p as a string  "(X, Y)".
+func (p Point) StringBrackets() string {
+	return fmt.Sprintf("(%d, %d)", p.X, p.Y)
+}
+
+// StringCompact returns a compact string representation of point p "X,Y".
+func (p Point) StringCompact() string {
+	return fmt.Sprintf("%d,%d", p.X, p.Y)
+}
+
+// Sub returns the difference of p and q.
+func (p Point) Sub(p2 Point) Point {
+	return Pt(p.X-p2.X, p.Y-p2.Y)
+}
+
+// MinMaxPoints returns the extremes of all the given points.
+func MinMaxPoints(p ...Point) (min Point, max Point) {
+	if 0 == len(p) {
+		return Point{}, Point{}
+	}
+	min, max = p[0], p[0]
+	for i := 1; i < len(p); i++ {
+		var pt = p[i]
+		if pt.X < min.X {
+			min.X = pt.X
+		} else if pt.X > max.X {
+			max.X = pt.X
+		}
+		if pt.Y < min.Y {
+			min.Y = pt.Y
+		} else if pt.Y > max.Y {
+			max.Y = pt.Y
+		}
+	}
+	return min, max
 }