Skip to main content Module math_functions Copy item path Source Aabb Axis aligned bounding box. CosSin Cosine and sine pair.
This uses a custom implementation designed for cross-platform determinism. Mat2 A 2x2 matrix stored as columns. Ported from math_internal.h for tests and
internal use (b3Matrix2). Matrix3 A 3x3 matrix. Plane A plane.
separation = dot(normal, point) - offset Quat A quaternion. SegmentDistanceResult The closest points between two segments or infinite lines. Transform A rigid transform. Triangle A triangle with vertex indices and edge flags.
(math_internal.h: b3Triangle) TrianglePoint Closest point on a triangle and the feature that owns it.
(math_internal.h: b3TrianglePoint) Vec2 A 2D vector. Vec3 A 3D vector. BOUNDS3_EMPTY Empty AABB (inverted bounds). (math_internal.h: B3_BOUNDS3_EMPTY) DEG_TO_RAD Convenience constant to convert from degrees to radians. (B3_DEG_TO_RAD) MAT2_ZERO Zero 2x2 matrix. (math_internal.h literal) MAT3_IDENTITY MAT3_ZERO MIN_SCALE Minimum scale used for scaling collision meshes, etc. (B3_MIN_SCALE) PI https://en.wikipedia.org/wiki/Pi
The C B3_PI literal (3.14159265359f) rounds to exactly this f32 value.POS_ZERO QUAT_IDENTITY RAD_TO_DEG Convenience constant to convert from radians to degrees. (B3_RAD_TO_DEG) SQRT3 √3. (math_internal.h: B3_SQRT3) TRANSFORM_IDENTITY TWO_PI 2π. (math_internal.h: B3_TWO_PI) VEC2_ZERO VEC3_AXIS_X VEC3_AXIS_Y VEC3_AXIS_Z VEC3_ONE VEC3_ZERO WORLD_TRANSFORM_IDENTITY aabb_add_point Add a point to an AABB. (math_internal.h: b3AABB_AddPoint) aabb_area Get the surface area of an axis-aligned bounding box. aabb_center Get the center of an axis-aligned bounding box. aabb_contains Does a fully contain b? aabb_extents Get the extents (half-widths) of an axis-aligned bounding box. aabb_inflate Add uniform padding to an axis-aligned bounding box. aabb_overlaps Do two axis-aligned boxes overlap? aabb_transform Transform an axis-aligned bounding box. This can create a larger box
than if you recomputed the AABB of the original shape with the transform
applied. aabb_union Get the union of two axis-aligned bounding boxes. abs Component-wise absolute value. abs_float @return the absolute value of a float. abs_matrix3 Get the component-wise absolute value of a matrix. add Vector addition. add2 2D vector addition. (math_internal.h: b3Add2) add_mm Matrix addition.
@return a + b align_up8 Align x up to a multiple of 8. (math_internal.h: b3AlignUp8) arbitrary_perp Assume v is a unit vector. (math_internal.h: b3ArbitraryPerp) atan2 Compute an approximate arctangent in the range [-pi, pi]
This is hand coded for cross-platform determinism. The atan2f
function in the standard library is not cross-platform deterministic.
Accurate to around 0.0023 degrees. blend2 Blend two vectors: s * a + t * b blend3 Blend three vectors: s * a + t * b + u * c. (math_internal.h: b3Blend3) box_inertia Box inertia about the center for an AABB from min to max.
(math_functions.c: b3BoxInertia) clamp Component-wise clamped value. clamp_float @return a float clamped between a lower and upper bound. clamp_int @return an integer clamped between a lower and upper bound. closest_point_on_triangle Closest point on triangle ABC to query point Q (Ericson §5.1.5).
(math_functions.c: b3ClosestPointOnTriangle) closest_point_to_aabb Get the closest point on an axis-aligned bounding box. compute_cos_sin Compute the cosine and sine of an angle in radians. Implemented
for cross-platform determinism. compute_quat_between_unit_vectors Find a quaternion that rotates one vector to another. conjugate Quaternion conjugate (cheap inverse). cos @deprecated cross https://en.wikipedia.org/wiki/Cross_product cross2 2D cross product (scalar). (math_internal.h: b3Cross2) cylinder_inertia Solid cylinder inertia about its center, axis along Y.
(math_functions.c: b3CylinderInertia) delta_quat_to_rotation Pseudo angular velocity from a quaternion target.
w = 2 * (target - q) * conj(q) (math_internal.h: b3DeltaQuatToRotation) det Compute the determinant of a 3-by-3 matrix. distance Distance between two points. distance_squared Squared distance between two points. distance_squared2 2D distance squared. (math_internal.h: b3DistanceSquared2) dot Vector dot product. dot2 2D dot product. (math_internal.h: b3Dot2) dot_quat Compute dot product of two quaternions. Useful for polarity tests. get_axis_angle Get the axis and angle from a quaternion. Assumes the quaternion is normalized. get_by_index Get a Vec3 component by index. (math_internal.h: b3GetByIndex) get_length_and_normalize Normalize a vector and return the length. Returns a zero vector
if the input is very small. get_quat_angle Get the angle for a quaternion in radians get_swing_angle Swing angle used for cone limit get_twist_angle Twist angle around the z-axis, used for twist limit and revolute angle limit integrate_rotation Integrate rotation from angular velocity.
delta_rotation is the angular displacement in radians (ω · h).
q2 = q1 + 0.5 * omega * q1
(math_internal.h: b3IntegrateRotation) intersect_ray_triangle Intersect a ray with a triangle. Returns the hit fraction in (0, 1], or 1.0 on miss.
(simd.c: b3IntersectRayTriangle, scalar path) inv_mul_quat Compute a relative quaternion.
inv(q1) * q2 inv_mul_transforms Creates a transform that converts a local point in frame B to a local point in frame A.
This is useful for transforming points between the local spaces of two frames that are
in world space. inv_mul_world_transforms Relative transform of frame B in frame A. The narrow phase boundary. inv_rotate_vector Inverse rotate a vector. inv_transform_point Inverse transform a point. inv_transform_world_point Transform a world position to a local point. One double subtraction, then float. invert2 Invert a 2-by-2 matrix. (math_internal.h: b3Invert2) invert_matrix General matrix inverse. invert_t Invert a matrix (returns the adjugate / det without the final transpose of
invert_matrix invert_transform Get the inverse of a transform. is_bounded_aabb Is this AABB reasonably close to the origin? See B3_HUGE. is_normalized Is a vector normalized? In other words, does it have unit length? is_normalized_quat Does the supplied quaternion have unit length? is_sane_aabb Is this AABB valid and reasonable? is_valid_aabb Is this a valid bounding box? Not Nan or infinity. Upper bound greater than or equal to lower bound. is_valid_float Is this a valid number? Not NaN or infinity. is_valid_matrix3 Is this a valid matrix? Not NaN or infinity. is_valid_plane Is this a valid plane? Normal is a unit vector. Not Nan or infinity. is_valid_position Is this a valid world position? Not NaN or infinity. is_valid_quat Is this a valid quaternion? Not NaN or infinity. Is normalized. is_valid_transform Is this a valid transform? Not NaN or infinity. Is normalized. is_valid_vec3 Is this a valid vector? Not NaN or infinity. is_valid_world_transform Is this a valid world transform? Not NaN or infinity. Rotation is normalized. is_within_segments True if both closest-point fractions lie on their segments. (math_internal.h: b3IsWithinSegments) length Vector length. length2 2D length. (math_internal.h: b3Length2) length_squared Vector length squared. length_squared2 2D length squared. (math_internal.h: b3LengthSquared2) lerp Linearly interpolate between two vectors. lerp_float Interpolate a scalar. lerp_position World position interpolation for sweeps and sampling. line_distance Compute the closest points on two infinite lines. major_axis Major axis of a vector (same as max_element_index make_aabb Get the AABB of a point cloud. make_diagonal_matrix Diagonal matrix. (math_internal.h: b3MakeDiagonalMatrix) make_matrix_from_quat Make a matrix from a quaternion. This is useful if you need to
rotate many vectors. make_normal_from_points Unit normal from three points. (math_internal.h: b3MakeNormalFromPoints) make_plane_from_normal_and_point Plane through point with given normal. (math_internal.h: b3MakePlaneFromNormalAndPoint) make_plane_from_points Plane through three points. (math_internal.h: b3MakePlaneFromPoints) make_quat_from_axis_angle Make a quaternion that is equivalent to rotating around an axis by a specified angle. make_quat_from_matrix Extract a quaternion from a rotation matrix. make_world_transform Promote a float transform to a world transform. Lossless. max Component-wise maximum value. max_element_index Index of the largest component. (math_internal.h: b3MaxElementIndex) max_float @return the maximum of two floats. max_int @return the maximum of two integers. min Component-wise minimum value. min_float @return the minimum of two floats.
Matches the C ternary exactly, including NaN propagation (a < b is false for NaN). min_int @return the minimum of two integers. modified_cross Component-wise product sum used for AABB extent under rotation.
(math_internal.h: b3ModifiedCross) mul Vector component-wise multiplication. mul_add a + s * b mul_mm Matrix multiplication.
@return a * b mul_mm2 Multiply two 2-by-2 matrices. (math_internal.h: b3MulMM2) mul_mv Multiply a matrix times a column vector. mul_mv2 Multiply a 2-by-2 matrix times a 2D vector. (math_internal.h: b3MulMV2) mul_mv2_sym Symmetric 2×2 × vector matching b3MulMV2W (cxx=cx.x, cxy=cx.y, cyy=cy.y). mul_mv_sym Symmetric matrix × vector matching b3MulMVW under B3_SIMD_NONE. mul_quat Multiply two quaternions. mul_sm Multiply a matrix by a scalar, component-wise. mul_sub a - s * b mul_sv s * a mul_sv2 2D scalar multiply. (math_internal.h: b3MulSV2) mul_transforms Multiply two transforms. If the result is applied to a point p local to frame B,
the transform would first convert p to a point local to frame A, then into a point
in the world frame. This is useful if frame B is a child of frame A. mul_world_transforms Compose a world transform with a local transform. neg Vector negation. negate_mat3 Negate a matrix. negate_quat Component-wise quaternion negation. nlerp Linearly interpolate and normalize between two quaternions normalize Normalize a vector. Returns a zero vector if the input vector is very small. normalize_quat Normalize a quaternion. offset_aabb Translate a local AABB by a world origin, rounding outward so the float box always contains
the double box. Far from the origin a plain conversion could clip a shape out of its own box.
In float mode the origin is float and the rounding is a no-op. offset_pos p + d perp Get a unit vector that is perpendicular to the supplied vector. plane_separation Signed separation of a point from a plane. (math_internal.h: b3PlaneSeparation) point_to_segment_distance Compute the closest point on the segment a-b to the target q. rotate_inertia Rotate a central inertia tensor by a quaternion. (math_internal.h: b3RotateInertia) rotate_vector Rotate a vector. round_down_float round_up_float safe_scale Create a safe scaling value for scaling collision. This allows
negative scale, but keeps scale sufficiently far from zero. scalar_triple_product Scalar triple product a · (b × c). (math_internal.h: b3ScalarTripleProduct) segment_distance Compute the closest points on two line segments. sign Component-wise -1 or 1 (1 if zero). signed_volume Negative if p is below the triangle v1-v2-v3. (math_internal.h: b3SignedVolume) sin @deprecated skew Skew-symmetric cross-product matrix. (math_internal.h: b3Skew) solve2 Solve A * x = b for a 2-by-2 matrix. Assumes positive semi-definite.
(math_internal.h: b3Solve2) solve3 Solve a matrix equation.
@return inv(m) * a sphere_inertia Solid sphere inertia about its center. (math_functions.c: b3SphereInertia) steiner Get the inertia tensor of an offset point.
https://en.wikipedia.org/wiki/Parallel_axis_theorem sub Vector subtraction. sub2 2D vector subtraction. (math_internal.h: b3Sub2) sub_mm Matrix subtraction.
@return a - b sub_pos a - b, demoted to float. The primary precision boundary operation. test_bounds_overlap Test overlap between two AABBs given as min/max corners.
(simd.h: b3TestBoundsOverlap) test_bounds_ray_overlap Test a ray for edge separation with an AABB (Gino, p80).
(simd.h: b3TestBoundsRayOverlap) test_bounds_triangle_overlap Test overlap between an AABB (center + extent) and a triangle.
(simd.c: b3TestBoundsTriangleOverlap) to_pos Convert a vector to a world position. to_relative_transform Shift a world transform into the frame of a base position. to_vec3 Lossy conversion of a world position to a float vector. transform_plane Transform a plane by a rigid transform. (math_internal.h: b3TransformPlane) transform_point Transform a point. transform_world_point Transform a local point to a world position. Rotation in float, translation in double. transpose Matrix transpose. unwind_angle Convert any angle into the range [-pi, pi]. Pos WorldTransform