Implement vec3 scalar and vector product, product by a scalar, get unit vector and print to ostream.

Fix wrong vec3 norm implementation.

2 files changed, 93 insertions, 17 deletions

diff --git a/test.cpp b/test.cpp
index 8f413f3..8c450f9 100644
--- a/test.cpp
+++ b/test.cpp
@@ -24,11 +24,47 @@ TEST(Vec, VecMin) {
     ASSERT_EQ(d + (-e), f);
 }
 
-TEST(Vec, VecCrossProduct) {
+TEST(Vec, CrossProduct) {
     vec3i a{1, 1, 1}, b{2, 2, 2}, c{3, 4, 5}, d{6, 7, 8}, e{-3, -6, -3};
-    ASSERT_EQ(a * b, vec3i{});
-    ASSERT_EQ(c * d, e);
+    ASSERT_EQ(cross(a, b), vec3i{});
+    ASSERT_EQ(a.cross(b), vec3i{});
+    ASSERT_EQ(cross(c, d), e);
+    ASSERT_EQ(c.cross(d), e);
 
-    vec3d f{3.0, 4.0, 5.0}, g{6.0, 7.0, 8.0}, h{-3, -6, -3};
-    ASSERT_EQ(f * g, h);
+    vec3d f{3, 4, 5}, g{6, 7, 8}, h{-3, -6, -3};
+    ASSERT_EQ(cross(f, g), h);
+    ASSERT_EQ(f.cross(g), h);
+}
+
+TEST(Vec, DotProduct) {
+    vec3i c{3, 4, 5}, d{6, 7, 8};
+    int e = 18 + 28 + 40;
+    ASSERT_EQ(dot(c, d), e);
+    ASSERT_EQ(c.dot(d), e);
+
+    vec3d f{3, 4, 5}, g{6, 7, 8};
+    ASSERT_EQ(dot(f, g), e);
+    ASSERT_EQ(f.dot(g), e);
+}
+
+TEST(Vec, MulByScalar) {
+    vec3i a{1, 1, 1}, b{2, 2, 2};
+    vec3d c{7, 14, 21}, d{1, 2, 3};
+    ASSERT_EQ(a * 2, b);
+    ASSERT_EQ(a / 0.5, b);
+    ASSERT_EQ(2 * a, b);
+    ASSERT_EQ(c * (1.0 / 7), d);
+    ASSERT_EQ(c / 7, d);
+    ASSERT_EQ(c / 7.0, d);
+}
+
+TEST(Vec, Norm) {
+    vec3d a{1, 1, 1}, b{2, 2, 2};
+    ASSERT_EQ(a.norm(), sqrt(3));
+    ASSERT_EQ(b.norm(), sqrt(12));
+}
+
+TEST(Vec, UnitVec) {
+    vec3d a{1, 2, 2}, b{1.0 / 3, 2.0 / 3, 2.0 / 3};
+    ASSERT_EQ(a.unit_vec(), b);
 }
\ No newline at end of file
diff --git a/vec.h b/vec.h
index ac6ea44..ad5f727 100644
--- a/vec.h
+++ b/vec.h
@@ -36,35 +36,75 @@ struct vec3 {
     }
 
     vec3 operator-(const vec3 &b) const {
-        return vec3{.x=x - b.x, .y=y - b.y, .z=z - b.z};
-    }
-
-    // cross product
-    vec3 operator*(const vec3 &b) const {
-        return vec3{.x=y * b.z - z * b.y, .y=x * b.z - z * b.x, .z=x * b.y - y * b.x};
+        return *this + (-b);
     }
 
     bool operator==(const vec3 b) const {
         return eq(x, b.x) && eq(y, b.y) && eq(z, b.z);
     }
 
-    // dot product
-    int dot(const vec3 &b) const {
+    // dot product (aka inner product, or scalar product, producing a scalar)
+    T dot(const vec3 &b) const {
         return x * b.x + y * b.y + z * b.z;
     }
 
+    // cross product (aka outer product, or vector product, producing a vector)
+    vec3 cross(const vec3 &b) const {
+        return vec3{.x=y * b.z - z * b.y, .y=x * b.z - z * b.x, .z=x * b.y - y * b.x};
+    }
+
     // norm value
-    int norm(const int level = 2) const {
+    double norm(const int level = 2) const {
         if (level == 2) {
-            return std::abs(x * x + y * y + z * z);
+            return std::abs(sqrt(x * x + y * y + z * z));
         } else if (level == 1) {
-            return std::abs(x + y + z);
+            return std::abs(x) + std::abs(y) + std::abs(z);
         } else {
-            return (int) std::abs(powl(x, level) + powl(y, level) + powl(z, level));
+            return powl(powl(x, level) + powl(y, level) + powl(z, level), 1.0 / level);
         }
     }
+
+    vec3 unit_vec() const {
+        return *this * (1.0 / norm());
+    }
 };
 
+// print to ostream
+template<typename T>
+std::ostream &operator<<(std::ostream &out, const vec3<T> &vec) {
+    return out << "vec3[x=" << vec.x << ", y=" << vec.y << ", z=" << vec.z << ']';
+}
+
+// product vec3 by a scalar
+template<typename T, typename S>
+vec3<T> operator*(const vec3<T> &vec, const S &b) {
+    return vec3<T>{.x=(T) (vec.x * b), .y=(T) (vec.y * b), .z=(T) (vec.z * b)};
+}
+
+// product vec3 by a scalar
+template<typename T, typename S>
+vec3<T> operator*(const S &b, const vec3<T> &vec) {
+    return vec3<T>{.x=(T) (vec.x * b), .y=(T) (vec.y * b), .z=(T) (vec.z * b)};
+}
+
+// product vec3 by the inversion of a scalar (div by a scalar)
+template<typename T, typename S>
+vec3<T> operator/(const vec3<T> &vec, const S &b) {
+    return vec3<T>{.x=(T) (vec.x / b), .y=(T) (vec.y / b), .z=(T) (vec.z / b)};
+}
+
+// scalar product (inner product)
+template<typename T>
+T dot(const vec3<T> &a, const vec3<T> &b) {
+    return a.dot(b);
+}
+
+// vector product (outer product)
+template<typename T>
+vec3<T> cross(const vec3<T> &a, const vec3<T> &b) {
+    return a.cross(b);
+}
+
 // 3-dim vector (int)
 using vec3i = vec3<int>;