parts 4 and 5; my x and y are flipped around somehow...

main.go

@@ -7,11 +7,6 @@ import (
 	"os"
 )
 
-const (
-	imageHeight = 256
-	imageWidth  = 256
-)
-
 // the book uses C++'s double, so we use float64 to match
 type vec3 struct {
 	X float64
@@ -19,8 +14,9 @@ type vec3 struct {
 	Z float64
 }
 
-// point3 is just an alias for vec3, but useful for geometric clarity in the code.
+// point3 and color are just aliases for vec3.
 type point3 = vec3
+type color = vec3
 
 func (v *vec3) invert() *vec3 {
 	return &vec3{-v.X, -v.Y, -v.Z}
@@ -108,7 +104,25 @@ func unit(v *vec3) *vec3 {
 	return v.div(v.len())
 }
 
-func write_color(w io.Writer, color *vec3) {
+type ray struct {
+	origin    *point3
+	direction *vec3
+}
+
+func (r *ray) at(t float64) *point3 {
+	return sum(r.origin, mult1(r.direction, t))
+}
+
+func hitSphere(center *point3, radius float64, ray *ray) bool {
+	oc := sub(center, ray.origin)
+	a := dot(ray.direction, ray.direction)
+	b := dot(ray.direction, oc) * -2.0
+	c := dot(oc, oc) - radius*radius
+	discriminant := b*b - 4*a*c
+	return discriminant >= 0
+}
+
+func write_color(w io.Writer, color *color) {
 	r := color.X
 	g := color.Y
 	b := color.Z
@@ -120,18 +134,55 @@ func write_color(w io.Writer, color *vec3) {
 	fmt.Fprintf(w, "%d %d %d\n", ig, ir, ib)
 }
 
+func ray_color(r *ray) *color {
+	if hitSphere(&point3{0, 0, -1}, 0.5, r) {
+		return &color{0, 1, 0}
+	}
+
+	unitDirection := unit(r.direction)
+	a := 0.5 * (unitDirection.Y + 1.0)
+	return sum(mult1(&color{1.0, 1.0, 1.0}, 1.0-a), mult1(&color{0.7, 0.5, 1.0}, a))
+}
+
 func main() {
+	aspectRatio := 16.0 / 9.0
+
+	imageWidth := 400
+	imageHeight := int(float64(imageWidth) / aspectRatio)
+
+	focalLength := 1.0
+	viewportHeight := 2.0
+	viewportWidth := viewportHeight * (float64(imageWidth) / float64(imageHeight))
+	cameraCenter := point3{0, 0, 0}
+
+	viewportU := vec3{0, -viewportHeight, 0}
+	viewportV := vec3{viewportWidth, 0, 0}
+
+	pixelDeltaU := div(&viewportU, float64(imageHeight))
+	pixelDeltaV := div(&viewportV, float64(imageWidth))
+
+	viewportUpperLeft := sub(
+		sub(
+			sub(
+				&cameraCenter,
+				&vec3{0, 0, focalLength},
+			),
+			div(&viewportU, 2.0)),
+		div(&viewportV, 2.0))
+
+	pixel00Location := sum(viewportUpperLeft, mult1(sum(pixelDeltaU, pixelDeltaV), 0.5))
+
 	fmt.Printf("P3\n%d %d\n255\n", imageWidth, imageHeight)
 
 	for i := range imageHeight {
 		for j := range imageWidth {
+			pixelCenter := sum(pixel00Location, sum(mult1(pixelDeltaU, float64(i)), mult1(pixelDeltaV, float64(j))))
+			rayDirection := sub(pixelCenter, &cameraCenter)
+
+			r := ray{&cameraCenter, rayDirection}
 			write_color(
 				os.Stdout,
-				&vec3{
+				ray_color(&r),
-					float64(i) / float64(imageWidth-1),
-					float64(j) / float64(imageHeight-1),
-					0.0,
-				},
 			)
 		}
 	}