typed-geometry

Header-only strongly typed math library for graphics and geometry.

Usage / Example

Type definitions only, no functions:

#include <tg/typed-geometry.hh>

All functionality:

#include <tg/typed-geometry.hh>

tg::vec3 v;
tg::pos3 p;

// TODO

Most functionality is implemented as free functions, overloaded by type and with consistent vocabulary:

Vectors

Types vec3, ivec4, dvec2, ...

• normalize(a): returns normalized version of a
• dot(a, b): dot product
• cross(a, b): cross product
• component-wise math functions: sin, cos, abs, sqrt, ...

Transformations

• Matrix types mat3, imat3x4, ...
• Quaternion types quat, dquat, ...
• Transform types transform3, dtransform2, ...

Objects

Types pos3, iline2, ray3, dbox2, ...

Represent individual points or sets of points.

• contains(a, b): true iff a contains b (i.e. if each point in b is also contained in a)
• intersects(a, b): true iff a and b intersect (i.e. if at least one point is in a and in b)
• intersection(a, b): returns the appropriate object describing the intersection of two objects

Interpolation

• mix(a, b, t): linearly interpolates a and b with parameter t from 0..1.
• lerp(a, b, t): same as mix
• slerp(a, b, t): same as mix but with spherical interpolation (i.e. for quaternions)
• smoothstep(x0, x1, x): see GLSL smoothstep
• smootherstep(x0, x1, x): see GLSL smootherstep
• lmap(x, {x0_from, x1_from}, {x0_to, x1_to}): linearly maps a value from one range to another

TODO: splines

Random

• uniform(rng, a): uniformly samples a point from the object a
• uniform(rng, a, b): same as mix(a, b, uniform(t, 0.0f, 1.0f))

Naming Scheme

• foo(a, b) should read in the same order as english
• if not possible, a.foo(b) should make sense (e.g. contains(a, b) is interpreted as a.contains(b))
• if still ambiguous: faster changing parameters go last (e.g. coordinates(tri, point) or mix(a, b, t))

Dependencies

None.

TODO

• Benchmark how compile times are affected by includes / templates
• Add tests that verify optimal assembly generated
• Fractional and bigint data types
• Deduction guides