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Refactor moving sphere to use ray for center
This basically implements Peter's original alternative of having spheres always support animation, with static spheres as a special case. In this case, using a ray to represent the sphere center allows for pretty trivial selection of the center position at a given time, and simplifies the code.
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‎CHANGELOG.md

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@@ -13,6 +13,7 @@ Change Log / Ray Tracing in One Weekend
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- Change -- Include hittable.h from material.h; drop `hit_record` forward declaration (#1609)
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- Fix -- Slight improvement to `rotate_y::hit()` function (#1484)
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- Fix -- Fixed possible bogus values from `random_unit_vector()` due to underflow (#1606)
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- Change -- Refactor sphere to use ray representation for animate center (#1621)
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### In One Weekend
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- Fix -- Fixed usage of the term "unit cube" for a cube of diameter two (#1555, #1603)

‎books/RayTracingTheNextWeek.html

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@@ -176,70 +176,67 @@
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----------------------
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Now to create a moving object. I’ll update the sphere class so that its center moves linearly from
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`center1` at time=0 to `center2` at time=1. (It continues on indefinitely outside that time
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interval, so it really can be sampled at any time.)
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interval, so it really can be sampled at any time.) We'll do this by replacing the 3D center point
180+
with a 3D ray that describes the original position at time=0 and the displacement to the end
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position at time=1.
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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class sphere : public hittable {
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public:
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
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// Stationary Sphere
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sphere(const point3& center, double radius, shared_ptr<material> mat)
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: center1(center), radius(std::fmax(0,radius)), mat(mat), is_moving(false) {}
188+
sphere(const point3& static_center, double radius, shared_ptr<material> mat)
189+
: center(static_center, vec3(0,0,0)), radius(std::fmax(0,radius)), mat(mat) {}
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189191
// Moving Sphere
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sphere(const point3& center1, const point3& center2, double radius,
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shared_ptr<material> mat)
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: center1(center1), radius(std::fmax(0,radius)), mat(mat), is_moving(true)
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{
194-
center_vec = center2 - center1;
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}
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: center(center1, center2 - center1), radius(std::fmax(0,radius)), mat(mat) {}
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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...
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private:
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
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point3 center1;
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ray center;
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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double radius;
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shared_ptr<material> mat;
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
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bool is_moving;
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vec3 center_vec;
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point3 sphere_center(double time) const {
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// Linearly interpolate from center1 to center2 according to time, where t=0 yields
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// center1, and t=1 yields center2.
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return center1 + time*center_vec;
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}
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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};
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#endif
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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[Listing [moving-sphere]: <kbd>[sphere.h]</kbd> A moving sphere]
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An alternative to making special stationary spheres is to just make them all move, but stationary
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spheres have the same begin and end position. I’m on the fence about that trade-off between simpler
224-
code and more efficient stationary spheres, so let your design taste guide you.
225-
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<div class='together'>
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The updated `sphere::hit()` function is almost identical to the old `sphere::hit()` function:
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`center` just needs to query a function `sphere_center(time)`:
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we just need to now determine the current position of the animated center:
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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class sphere : public hittable {
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public:
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...
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bool hit(const ray& r, interval ray_t, hit_record& rec) const override {
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
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point3 center = is_moving ? sphere_center(r.time()) : center1;
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point3 current_center = center.at(r.time());
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vec3 oc = current_center - r.origin();
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
238-
vec3 oc = center - r.origin();
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auto a = r.direction().length_squared();
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auto h = dot(r.direction(), oc);
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auto c = oc.length_squared() - radius*radius;
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242228
...
229+
230+
rec.t = root;
231+
rec.p = r.at(rec.t);
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
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vec3 outward_normal = (rec.p - current_center) / radius;
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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rec.set_face_normal(r, outward_normal);
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get_sphere_uv(outward_normal, rec.u, rec.v);
237+
rec.mat = mat;
238+
239+
return true;
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}
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...
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};
@@ -711,12 +708,12 @@
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class sphere : public hittable {
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public:
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// Stationary Sphere
714-
sphere(const point3& center, double radius, shared_ptr<material> mat)
711+
sphere(const point3& static_center, double radius, shared_ptr<material> mat)
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
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: center1(center), radius(std::fmax(0,radius)), mat(mat), is_moving(false)
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: center(static_center, vec3(0,0,0)), radius(std::fmax(0,radius)), mat(mat)
717714
{
718715
auto rvec = vec3(radius, radius, radius);
719-
bbox = aabb(center1 - rvec, center1 + rvec);
716+
bbox = aabb(static_center - rvec, static_center + rvec);
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}
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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@@ -728,11 +725,9 @@
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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private:
731-
point3 center1;
728+
ray center;
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double radius;
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shared_ptr<material> mat;
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bool is_moving;
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vec3 center_vec;
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
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aabb bbox;
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
@@ -754,17 +749,15 @@
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// Moving Sphere
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sphere(const point3& center1, const point3& center2, double radius,
756751
shared_ptr<material> mat)
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: center1(center1), radius(std::fmax(0,radius)), mat(mat), is_moving(true)
758-
{
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
753+
: center(center1, center2 - center1), radius(std::fmax(0,radius)), mat(mat)
754+
{
760755
auto rvec = vec3(radius, radius, radius);
761-
aabb box1(center1 - rvec, center1 + rvec);
762-
aabb box2(center2 - rvec, center2 + rvec);
756+
aabb box1(center.at(0) - rvec, center.at(0) + rvec);
757+
aabb box2(center.at(1) - rvec, center.at(1) + rvec);
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bbox = aabb(box1, box2);
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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766-
center_vec = _center2 - _center1;
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}
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
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...
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};
@@ -1649,7 +1642,7 @@
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16501643
rec.t = root;
16511644
rec.p = r.at(rec.t);
1652-
vec3 outward_normal = (rec.p - center) / radius;
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vec3 outward_normal = (rec.p - current_center) / radius;
16531646
rec.set_face_normal(r, outward_normal);
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
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get_sphere_uv(outward_normal, rec.u, rec.v);

‎books/RayTracingTheRestOfYourLife.html

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@@ -3771,14 +3771,15 @@
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if (!this->hit(ray(origin, direction), interval(0.001, infinity), rec))
37723772
return 0;
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3774-
auto cos_theta_max = std::sqrt(1 - radius*radius/(center1 - origin).length_squared());
3774+
auto dist_squared = (center.at(0) - origin).length_squared();
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auto cos_theta_max = std::sqrt(1 - radius*radius/dist_squared);
37753776
auto solid_angle = 2*pi*(1-cos_theta_max);
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37773778
return 1 / solid_angle;
37783779
}
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37803781
vec3 random(const point3& origin) const override {
3781-
vec3 direction = center1 - origin;
3782+
vec3 direction = center.at(0) - origin;
37823783
auto distance_squared = direction.length_squared();
37833784
onb uvw(direction);
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return uvw.transform(random_to_sphere(radius, distance_squared));

‎src/TheNextWeek/sphere.h

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@@ -17,29 +17,27 @@
1717
class sphere : public hittable {
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public:
1919
// Stationary Sphere
20-
sphere(const point3& center, double radius, shared_ptr<material> mat)
21-
: center1(center), radius(std::fmax(0,radius)), mat(mat), is_moving(false)
20+
sphere(const point3& static_center, double radius, shared_ptr<material> mat)
21+
: center(static_center, vec3(0,0,0)), radius(std::fmax(0,radius)), mat(mat)
2222
{
2323
auto rvec = vec3(radius, radius, radius);
24-
bbox = aabb(center1 - rvec, center1 + rvec);
24+
bbox = aabb(static_center - rvec, static_center + rvec);
2525
}
2626

2727
// Moving Sphere
2828
sphere(const point3& center1, const point3& center2, double radius,
2929
shared_ptr<material> mat)
30-
: center1(center1), radius(std::fmax(0,radius)), mat(mat), is_moving(true)
30+
: center(center1, center2 - center1), radius(std::fmax(0,radius)), mat(mat)
3131
{
3232
auto rvec = vec3(radius, radius, radius);
33-
aabb box1(center1 - rvec, center1 + rvec);
34-
aabb box2(center2 - rvec, center2 + rvec);
33+
aabb box1(center.at(0) - rvec, center.at(0) + rvec);
34+
aabb box2(center.at(1) - rvec, center.at(1) + rvec);
3535
bbox = aabb(box1, box2);
36-
37-
center_vec = center2 - center1;
3836
}
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4038
bool hit(const ray& r, interval ray_t, hit_record& rec) const override {
41-
point3 center = is_moving ? sphere_center(r.time()) : center1;
42-
vec3 oc = center - r.origin();
39+
point3 current_center = center.at(r.time());
40+
vec3 oc = current_center - r.origin();
4341
auto a = r.direction().length_squared();
4442
auto h = dot(r.direction(), oc);
4543
auto c = oc.length_squared() - radius*radius;
@@ -60,7 +58,7 @@ class sphere : public hittable {
6058

6159
rec.t = root;
6260
rec.p = r.at(rec.t);
63-
vec3 outward_normal = (rec.p - center) / radius;
61+
vec3 outward_normal = (rec.p - current_center) / radius;
6462
rec.set_face_normal(r, outward_normal);
6563
get_sphere_uv(outward_normal, rec.u, rec.v);
6664
rec.mat = mat;
@@ -71,19 +69,11 @@ class sphere : public hittable {
7169
aabb bounding_box() const override { return bbox; }
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7371
private:
74-
point3 center1;
72+
ray center;
7573
double radius;
7674
shared_ptr<material> mat;
77-
bool is_moving;
78-
vec3 center_vec;
7975
aabb bbox;
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81-
point3 sphere_center(double time) const {
82-
// Linearly interpolate from center1 to center2 according to time, where t=0 yields
83-
// center1, and t=1 yields center2.
84-
return center1 + time*center_vec;
85-
}
86-
8777
static void get_sphere_uv(const point3& p, double& u, double& v) {
8878
// p: a given point on the sphere of radius one, centered at the origin.
8979
// u: returned value [0,1] of angle around the Y axis from X=-1.

‎src/TheRestOfYourLife/sphere.h

Lines changed: 13 additions & 22 deletions
Original file line numberDiff line numberDiff line change
@@ -18,29 +18,27 @@
1818
class sphere : public hittable {
1919
public:
2020
// Stationary Sphere
21-
sphere(const point3& center, double radius, shared_ptr<material> mat)
22-
: center1(center), radius(std::fmax(0,radius)), mat(mat), is_moving(false)
21+
sphere(const point3& static_center, double radius, shared_ptr<material> mat)
22+
: center(static_center, vec3(0,0,0)), radius(std::fmax(0,radius)), mat(mat)
2323
{
2424
auto rvec = vec3(radius, radius, radius);
25-
bbox = aabb(center1 - rvec, center1 + rvec);
25+
bbox = aabb(static_center - rvec, static_center + rvec);
2626
}
2727

2828
// Moving Sphere
2929
sphere(const point3& center1, const point3& center2, double radius,
3030
shared_ptr<material> mat)
31-
: center1(center1), radius(std::fmax(0,radius)), mat(mat), is_moving(true)
31+
: center(center1, center2 - center1), radius(std::fmax(0,radius)), mat(mat)
3232
{
3333
auto rvec = vec3(radius, radius, radius);
34-
aabb box1(center1 - rvec, center1 + rvec);
35-
aabb box2(center2 - rvec, center2 + rvec);
34+
aabb box1(center.at(0) - rvec, center.at(0) + rvec);
35+
aabb box2(center.at(1) - rvec, center.at(1) + rvec);
3636
bbox = aabb(box1, box2);
37-
38-
center_vec = center2 - center1;
3937
}
4038

4139
bool hit(const ray& r, interval ray_t, hit_record& rec) const override {
42-
point3 center = is_moving ? sphere_center(r.time()) : center1;
43-
vec3 oc = center - r.origin();
40+
point3 current_center = center.at(r.time());
41+
vec3 oc = current_center - r.origin();
4442
auto a = r.direction().length_squared();
4543
auto h = dot(r.direction(), oc);
4644
auto c = oc.length_squared() - radius*radius;
@@ -61,7 +59,7 @@ class sphere : public hittable {
6159

6260
rec.t = root;
6361
rec.p = r.at(rec.t);
64-
vec3 outward_normal = (rec.p - center) / radius;
62+
vec3 outward_normal = (rec.p - current_center) / radius;
6563
rec.set_face_normal(r, outward_normal);
6664
get_sphere_uv(outward_normal, rec.u, rec.v);
6765
rec.mat = mat;
@@ -78,33 +76,26 @@ class sphere : public hittable {
7876
if (!this->hit(ray(origin, direction), interval(0.001, infinity), rec))
7977
return 0;
8078

81-
auto cos_theta_max = std::sqrt(1 - radius*radius/(center1 - origin).length_squared());
79+
auto dist_squared = (center.at(0) - origin).length_squared();
80+
auto cos_theta_max = std::sqrt(1 - radius*radius/dist_squared);
8281
auto solid_angle = 2*pi*(1-cos_theta_max);
8382

8483
return 1 / solid_angle;
8584
}
8685

8786
vec3 random(const point3& origin) const override {
88-
vec3 direction = center1 - origin;
87+
vec3 direction = center.at(0) - origin;
8988
auto distance_squared = direction.length_squared();
9089
onb uvw(direction);
9190
return uvw.transform(random_to_sphere(radius, distance_squared));
9291
}
9392

9493
private:
95-
point3 center1;
94+
ray center;
9695
double radius;
9796
shared_ptr<material> mat;
98-
bool is_moving;
99-
vec3 center_vec;
10097
aabb bbox;
10198

102-
point3 sphere_center(double time) const {
103-
// Linearly interpolate from center1 to center2 according to time, where t=0 yields
104-
// center1, and t=1 yields center2.
105-
return center1 + time*center_vec;
106-
}
107-
10899
static void get_sphere_uv(const point3& p, double& u, double& v) {
109100
// p: a given point on the sphere of radius one, centered at the origin.
110101
// u: returned value [0,1] of angle around the Y axis from X=-1.

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