Math and geometry

Fx2D's public math types are small extensions of Eigen types. Use FxVec2f for 2D values, and FxVec3f for a body's (x, y, theta) pose or (vx, vy, omega) velocity.

#include "Fx2D/Scene.h"  // brings in math, geometry, entities, and the solver

FxVec2f force{20.0f, 0.0f};
FxVec3f pose{2.0f, 1.0f, FxPif / 4.0f};

Keep angle units straight

Engine pose angles, angular velocity, joint angles, and FxAngleWrap() use radians. The vector helper named rotate() is the exception: it takes degrees for convenience. Prefer the explicit _rad version in physics code.

FxVec2f heading{1.0f, 0.0f};
FxVec2f quarter_turn = heading.rotate_rad(FxPif / 2.0f);
FxVec2f screen_turn  = heading.rotate(90.0f);  // degrees

float relative = FxAngleWrap(body_b->pose.theta() - body_a->pose.theta());

FxVec2f also supplies perp(), perpCW(), and a scalar 2D cross(). The inherited Eigen operations such as .dot(), .norm(), and .normalized() are available too.

Move between body and world space

Use the entity transform helpers instead of applying the pose manually. They account for both translation and rotation.

const FxVec2f local_thruster{0.4f, 0.0f};
const FxVec2f world_thruster = ship->to_world_frame(local_thruster);

ship->apply_force(FxVec2f{0.0f, 30.0f}, world_thruster);

const FxVec2f local_hit = ship->to_entity_frame(world_hit);

FxVec3f::xy() returns the position part of a pose; theta() is an alias for z(). Use get_xy() when you explicitly want a copy.

Build collision geometry

FxShape is the one shape type used for both collision and visual geometry. A shape is local to its entity; it follows the entity automatically after set_collision_geometry().

auto crate = std::make_shared<FxEntity>("crate");
crate->set_mass(2.0f);
crate->set_collision_geometry(FxShape(FxVec2f{1.2f, 0.8f}, 0.05f)); // rounded box
crate->set_inertia();
crate->set_init_pose(FxVec3f{0.0f, 3.0f, 0.0f});
scene.add_entity(crate);

Choose the constructor by the geometry you need:

Geometry	Constructor
Circle	FxShape(radius)
Capsule	FxShape(length, radius)
Edge	FxShape(point_a, point_b)
Chain terrain	FxShape::make_chain(points)
Convex polygon	FxShape(vertices, skin_radius)
Rectangle	FxShape(size, skin_radius)

Polygons must be convex. Rectangle and polygon vertices are recentered on construction; edges and chains preserve their authored points, making them suitable for static level geometry. Call set_inertia() after setting the collision geometry when the shape should determine the body's inertia.

Arrays for geometry batches

FxVec2fArray is an aligned FxArray<FxVec2f>, useful for polygon and chain points. It supports range-for iteration and vector operations across the whole array.

FxVec2fArray terrain = {
  {-8.0f, 0.0f}, {-2.0f, 0.5f}, {2.0f, -0.2f}, {8.0f, 1.0f},
};

ground->set_collision_geometry(FxShape::make_chain(terrain));

For every available helper, matrix type, and constructor overload, use the math reference or the generated Math.h symbols.