Add an alternative implementation for a tetrahedron

README.md

@@ -48,6 +48,8 @@ The output consists of a series of images, each depicting a layer of the solid,
 | `htetra1.solid` | Hollow Tetrahedron | A hollow tetrahedron stood on its edge |
 | `tetrahedron2.solid` | Tetrahedron | A tetrahedron stood on its base/vertex |
 | `htetra2.solid` | Hollow Tetrahedron | A hollow tetrahedron stood on its base/vertex |
+| `tetrahedron3.solid` | Tetrahedron | A tetrahedron stood on its base/vertex |
+| `htetra3.solid` | Hollow Tetrahedron | A hollow tetrahedron stood on its base/vertex |
 | `octahedron1.solid` | Octahedron | An octaheron stood on its vertex |
 | `hoctahedron1.solid` | Hollow Octahedron | A hollow octahedron stood on its vertex |
 | `sphere.solid` | Sphere | A sphere of radius s |

examples/htetra3.solid

@@ -0,0 +1,60 @@
+# Tetrahedron
+
+# Tetrahedron bounding box size:
+
+# Figure 1: Side View
+#
+#       *_        -
+#      /  \       ^
+#     / |  \_
+#    /  |    \    depth
+#   /   |     \_  v
+#  *----0-------* -
+#
+# Figure 2: Top View
+#
+#  *_B
+#  | \_
+#  |\  \_
+#  | \   \_
+#  |  \    \_
+#  |   \A    \__
+#  |<a> *-<b>-__*D
+#  |   /    _/
+#  |  /   _/
+#  | /  _/
+#  |/ _/
+#  |_/
+#  *C
+
+# From these diagrams, you can tell that the width is the height of an
+# equilateral triangle. If we assume the edge of the tetrahedron is s, then:
+
+define @ns s - 4
+define @half_height s / 2
+
+# For the depth, a few calculations are necessary:
+#
+# a + b = s * sin(⅓π)
+# a² + (s/2)² = b²
+define @a (s/2)*tan(⅙π)
+define @na (@ns/2)*tan(⅙π)
+define @b s * (sin(⅓π) - tan(⅙π)/2)
+# a² + d² = (s*sin(⅓π))²
+define @depth s * sqrt((sin(⅓π))^2 - ((1/2)*tan(⅙π))^2)
+define @ndepth @ns * sqrt((sin(⅓π))^2 - ((1/2)*tan(⅙π))^2)
+
+# Considering that the origin is in the center of the base, the min x is -a,
+# the min y is -s/2, and the min z is 0
+-@a < x < @b
+-@half_height < y < @half_height
+0 < z < @depth
+
+{{ρ ≤ @a * sec(φ - ⅓π) * (1 - z/@depth) ∧ φ ≥ 0 ∧ φ ≤ 2 * ⅓π} ∨ \
+{ρ ≤ @a * sec(φ - π) * (1 - z/@depth) ∧ {φ ≥ 2 * ⅓π ∨ φ ≤ -2 * ⅓π}} ∨ \
+{ρ ≤ @a * sec(φ + ⅓π) * (1 - z/@depth) ∧ φ ≤ 0 ∧ φ ≥ -2 * ⅓π} ∨ ρ = 0} \
+⊻ \
+{z ≥ 1 ∧ z ≤ @ndepth ∧ \
+{{ρ ≤ @na * sec(φ - ⅓π) * (1 - z/@ndepth) ∧ φ ≥ 0 ∧ φ ≤ 2 * ⅓π} ∨ \
+{ρ ≤ @na * sec(φ - π) * (1 - z/@ndepth) ∧ {φ ≥ 2 * ⅓π ∨ φ ≤ -2 * ⅓π}} ∨ \
+{ρ ≤ @na * sec(φ + ⅓π) * (1 - z/@ndepth) ∧ φ ≤ 0 ∧ φ ≥ -2 * ⅓π} ∨ ρ = 0}}

examples/tetrahedron3.solid

@@ -0,0 +1,52 @@
+# Tetrahedron
+
+# Tetrahedron bounding box size:
+
+# Figure 1: Side View
+#
+#       *_        -
+#      /  \       ^
+#     / |  \_
+#    /  |    \    depth
+#   /   |     \_  v
+#  *----0-------* -
+#
+# Figure 2: Top View
+#
+#  *_B
+#  | \_
+#  |\  \_
+#  | \   \_
+#  |  \    \_
+#  |   \A    \__
+#  |<a> *-<b>-__*D
+#  |   /    _/
+#  |  /   _/
+#  | /  _/
+#  |/ _/
+#  |_/
+#  *C
+
+# From these diagrams, you can tell that the width is the height of an
+# equilateral triangle. If we assume the edge of the tetrahedron is s, then:
+
+define @half_height s / 2
+
+# For the depth, a few calculations are necessary:
+#
+# a + b = s * sin(⅓π)
+# a² + (s/2)² = b²
+define @a (s/2)*tan(⅙π)
+define @b s * (sin(⅓π) - tan(⅙π)/2)
+# a² + d² = (s*sin(⅓π))²
+define @depth s * sqrt((sin(⅓π))^2 - ((1/2)*tan(⅙π))^2)
+
+# Considering that the origin is in the center of the base, the min x is -a,
+# the min y is -s/2, and the min z is 0
+-@a < x < @b
+-@half_height < y < @half_height
+0 < z < @depth
+
+{ρ ≤ @a * sec(φ - ⅓π) * (1 - z/@depth) ∧ φ ≥ 0 ∧ φ ≤ 2 * ⅓π} ∨ \
+{ρ ≤ @a * sec(φ - π) * (1 - z/@depth) ∧ {φ ≥ 2 * ⅓π ∨ φ ≤ -2 * ⅓π}} ∨ \
+{ρ ≤ @a * sec(φ + ⅓π) * (1 - z/@depth) ∧ φ ≤ 0 ∧ φ ≥ -2 * ⅓π} ∨ ρ = 0

src/astree.rs

@@ -6,6 +6,9 @@ pub enum FunctionType {
     Sin,
     Cos,
     Tan,
+    Sec,
+    Csc,
+    Cot,
     Asin,
     Acos,
     Atan,
@@ -41,6 +44,9 @@ impl FunctionData {
             FunctionType::Sin => Ok(value.sin()),
             FunctionType::Cos => Ok(value.cos()),
             FunctionType::Tan => Ok(value.tan()),
+            FunctionType::Sec => Ok(value.cos().recip()),
+            FunctionType::Csc => Ok(value.sin().recip()),
+            FunctionType::Cot => Ok(value.tan().recip()),
             FunctionType::Asin => Ok(value.asin()),
             FunctionType::Acos => Ok(value.acos()),
             FunctionType::Atan => Ok(value.atan()),

src/main.rs

@@ -144,6 +144,9 @@ pomelo! {
     %type   #[token("sin", |_| FunctionType::Sin)]
             #[token("cos", |_| FunctionType::Cos)]
             #[token("tan", |_| FunctionType::Tan)]
+            #[token("sec", |_| FunctionType::Sec)]
+            #[token("csc", |_| FunctionType::Csc)]
+            #[token("cot", |_| FunctionType::Cot)]
             #[token("asin", |_| FunctionType::Asin)]
             #[token("acos", |_| FunctionType::Acos)]
             #[token("atan", |_| FunctionType::Atan)]