godot-math

godot-math is a D port of Godot's linear algebra with unchanged semantics.

➡️ See Godot Math documentation

Using DUB you can add it to your project with:

"dependencies":
{
    "godot-math": "~>1.0"
}

dependency "godot-math" version="~>1.0"

Examples

Transform a point in 2D:

import godotmath;

// Create a Vector2
Vector2 v = Vector2(2.0f, 3.0f);

// Create a Transform2D: rotation by 45 degrees and translate by (1, 1)
float angle = GM_PI / 4;
Transform2D t2d = Transform2D(angle, Vector2(1, 1));
Vector2 v2 = t2d * v; // Apply the transform

Transform a point in 3D:

import godotmath;

auto proj = Projection.create_perspective(60.0f, 16.0f/9.0f, 0.1f, 100.0f);

// Transform a 3D point
Vector4 point = Vector4(5.0f, 3.0f, 10.0f, 1.0f);
Vector4 projected = proj * point;  // Apply transform

Why?

Godot's math API is well-tested and documented.

Godot's math bring helpful semantics to small vectors and matrices:

• A Transform2D/Transform3D is scaling + translation + rotation without shearing.
• A Projection is a 4x4 matrix scaling with potentially perspective transform.
• A Basis is a 3x3 matrix that only deals with base change / rotation.

Features

• one .d file
• Everything is pure nothrow @nogc @safe
• LDC, GDC (untested), DMD
• Uses numem and the C runtime only

Type	Status	Description	Documentation
Vector2	✅	2D float vector, or size, or point	Vector2
Vector3	✅	3D float vector, or size, or point	Vector3
Vector4	✅	4D float vector or point	Vector4
Vector2i	✅	2D int vector, or size, or point	Vector2i
Vector3i	✅	3D int vector, or size, or point	Vector3i
Vector4i	✅	4D int vector or point	Vector4i
Rect2	✅	2D float rectangle	Rect2
Rect2i	✅	2D int rectangle	Rect2i
Transform2D	✅	2x3 matrix (column-major)	Transform2D
Basis	✅	3x3 matrix (row-major)	Basis
Transform3D	✅	3x4 matrix (row-major)	Transform3D
Projection	✅	4x4 matrix (column-major)	Projection
Plane	✅	3D plane	Plane
AABB	✅	3D bounding box	AABB

Math functions

Note: When a float function exist, a double overload also exist with identical name.

float gm_abs(float x);
int   gm_abs(int x);
float gm_acos(float x);
float gm_acosh(float x);
float gm_angle_difference(float from, float to);
float gm_asin(float x);
float gm_asinh(float x);
float gm_atan(float x);
float gm_atan2(float y, float x);
float gm_bezier_derivative(float start, float control_1, float control_2, float end, float t);
float gm_bezier_interpolate(float start, float control_1, float control_2, float end, float t);
float gm_ceil(float x);
float gm_clamp(float value, float min, float max);
int   gm_clamp(int value, int min, int max);
float gm_cos(float x);
float gm_cubic_interpolate(float from, float to, float pre, float post, float weight);
float gm_cubic_interpolate_in_time(float from, float to, float pre, float post, float weight, float to_t, float pre_t, float post_t);
float gm_deg_to_rad(float y);
float gm_floor(float x);
float gm_fmod(float x, float y);
float gm_fposmod(float x, float y);
bool  gm_is_equal_approx(float left, float right);
bool  gm_is_equal_approx(float left, float right, float tolerance);
bool  gm_is_finite(float x);
bool  gm_is_zero_approx(float value);
float gm_lerp(float from, float to, float weight);
float gm_lerp_angle(float from, float to, float weight);
bool  gm_likely(bool b);
bool  gm_unlikely(bool b);
float gm_rad_to_deg(float y);
float gm_round(float x);
int   gm_sign(int v);
float gm_sign(float v);
bool  gm_signbit(float num);
bool  gm_signbit(double num);
float gm_sin(float x);
float gm_snapped(float value, float step);
int   gm_snapped(int value, int step);
float gm_sqrt(float x);
void  gm_swap(T)(ref T a, ref T b);
float gm_tan(float x);

Differing names

• Both float and double versions exist at once, with a ***d suffix (eg: Projectiond, Vector2d, Rect2d).
• In global scope, function symbols get a gm_ prefix.
• For vectors:
  • .clampf/.clampi replaced by overloaded .clamp
  • .snappedf / .snappedi replaced by overloaded .snapped.
  • .minf/.mini replaced by overloaded .min
  • .maxf/.maxi replaced by overloaded .max

Small semantic differences

• Rect2/Rect2i/Rect2d have a .merge_non_empty method that, in case of a union with an empty rectangle, return the other rectangle.
• Bonus methods for rectangles, such has .left, .top, .right, .bottom, .scale.
• Projection inverse is less precise than in original Godot. You can always go double to get more precise .inverse()