trigonometry

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layout: default title: Trigonometry

Trigonometry

Overview

Trigonometric functions, angle conversions, angle wrapping, and angular interpolation. All angle parameters are in radians unless noted.

Why Use This?

Game and graphics code constantly works with angles for rotation, field of view, arc calculations, and smooth angular interpolation.

Functions

Basic Trig

Function	Description
lm2_cos_f32(angle_rad)	Cosine
lm2_sin_f32(angle_rad)	Sine
lm2_tan_f32(angle_rad)	Tangent
lm2_acos_f32(value)	Inverse cosine
lm2_asin_f32(value)	Inverse sine
lm2_atan_f32(value)	Inverse tangent
lm2_atan2_f32(y, x)	Two-argument inverse tangent

Conversions

Function	Description
lm2_deg_to_rad_f32(degrees)	Degrees to radians
lm2_rad_to_deg_f32(radians)	Radians to degrees

Angle Operations (Radians)

Function	Description
lm2_wrap_rad_f32(angle)	Wrap angle to [-PI, PI]
lm2_shortest_rad_f32(from, to)	Shortest angular distance in [-PI, PI]
lm2_lerp_rad_f32(a, t, b)	Interpolate angles using shortest path

Angle Operations (Degrees)

Function	Description
lm2_wrap_deg_f32(angle)	Wrap angle to [-180, 180]
lm2_shortest_deg_f32(from, to)	Shortest angular distance in [-180, 180]
lm2_lerp_deg_f32(a, t, b)	Interpolate angles using shortest path

All functions are available in _f64 and _f32 variants.

Constants

Constant	Value	Description
LM2_PI_F32	3.14159...	PI
LM2_2PI_F32	6.28318...	2 * PI
LM2_HPI_F32	1.57079...	PI / 2
LM2_RAD_TO_DEG_F32	57.2957...	Radians-to-degrees multiplier
LM2_DEG_TO_RAD_F32	0.01745...	Degrees-to-radians multiplier
LM2_EULER_F32	0.57721...	Euler-Mascheroni constant
LM2_SQRT2_F32	1.41421...	Square root of 2
LM2_E_F32	2.71828...	Euler's number

All constants also available with _F64 suffix.

Example

float angle_deg = 270.0f;
float angle_rad = lm2_deg_to_rad_f32(angle_deg);
float wrapped = lm2_wrap_deg_f32(angle_deg); // -90

// Smoothly interpolate between two angles
float from = lm2_deg_to_rad_f32(350.0f);
float to   = lm2_deg_to_rad_f32(10.0f);
float mid  = lm2_lerp_rad_f32(from, 0.5f, to);  // goes through 0, not 180