typed-geometry

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

Usage / Example

Type definitions only, no functions:

#include <tg/typed-geometry-lean.hh>

All functionality:

#include <tg/typed-geometry.hh>

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

// TODO

Helpers for interacting with the standard library:

#include <tg/typed-geometry-std.hh>

tg::pos3 p;
std::cout << p;                    // std::operator<<(std::ostream&, ...)
std::map<p, int> v_cnts;           // std::less
std::unordered_map<p, int> v_cnts; // std::hash

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

Object Types

Basically all tg provided types are regular, i.e. have value semantics like int or vector. The following categories exist:

• POD types like vec and most fixed-size objects
• dynamically sized non-POD values like polygon (similar to vector)
• transparent types like vec where .x is part of the interface
• opaque types like angle and quadric where the representation is implementation detail

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

See docs/Objects.md for more information.

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

tg::rng rng;
auto v = uniform(rng, -1.0f, 1.0f);
auto p = uniform(rng, obj);

• 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))

C++ 17 Features

• deduction guides: auto v = tg::vec(1, 2.5f, 3), auto p = tg::pos(v);
• structured binding: auto [x, y, z] = tg::vec3(...)

Dependencies

None.

TODO

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