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Bounds And Geometry

FixedMathSharp geometry is dimension-explicit. The core package owns reusable fixed-point shape math only; physics concepts such as colliders, materials, shape casts, contact manifolds, body state, and broad-phase layers belong in higher-level.

Dimensional Ownership

Use 3D types for volume and spatial math:

  • FixedBoundBox: 3D axis-aligned bounding box.
  • FixedBoundSphere: 3D sphere bound.
  • FixedBoundFrustum: 3D frustum bound.
  • FixedRay: 3D ray intersection primitive.
  • FixedPlane: 3D plane classification primitive.
  • FixedSegment: finite 3D segment with closest-point, distance, and bounds.
  • FixedTriangle: ordered 3D triangle with area, normal, bounds, closest-point, containment, interpolation, and projected barycentric helpers.

Use 2D types for plane math:

  • FixedBoundArea: 2D Vector2d axis-aligned bounding area.
  • FixedBoundCircle: 2D circular bound.
  • FixedRay2d: 2D ray intersection primitive.
  • FixedSegment2d: finite 2D segment with closest-point, distance, and bounds.
  • FixedTriangle2d: ordered 2D triangle with signed area, bounds, closest-point, containment, interpolation, and barycentric helpers.

There is no 3D FixedBoundArea compatibility model. A flat world footprint should be represented as FixedBoundArea plus explicit layer, elevation, or height state in the consuming package. A volumetric query or collider bound should use FixedBoundBox.

Construction

FixedBoundBox and FixedBoundArea use named factories so call sites state the meaning of their extents:

FixedBoundBox box = FixedBoundBox.FromMinMax(min3d, max3d);
FixedBoundBox room = FixedBoundBox.FromCenterAndSize(center3d, size3d);
FixedBoundBox influence = FixedBoundBox.FromCenterAndScope(center3d, halfExtents3d);

FixedBoundArea area = FixedBoundArea.FromMinMax(min2d, max2d);
FixedBoundArea footprint = FixedBoundArea.FromCenterAndSize(center2d, size2d);
FixedBoundArea sensorArea = FixedBoundArea.FromCenterAndScope(center2d, halfExtents2d);

FromMinMax normalizes swapped inputs. FromCenterAndSize and FromCenterAndScope normalize negative extents by absolute component value. This keeps public bounds state canonical without asking every caller to sort or sanitize the inputs first.

FixedBoundCircle and FixedBoundSphere normalize radius by absolute value through construction, assignment, and serialized state load. FixedRay and FixedRay2d do not normalize direction; returned ray parameters are physical distances only when the direction is normalized by the caller.

Boundary Semantics

Default containment and intersection methods are boundary-inclusive:

  • Contains(point) returns true for points on edges, faces, or surfaces.
  • Intersects(...) treats touching edges, faces, corners, and tangent contact as intersections.
  • Ray-bound intersections can return Fixed64.Zero when the ray starts inside or on the queried shape.

Strict overlap methods exist only where downstream systems need to distinguish touching contact from positive area or volume overlap:

bool touchesOrOverlaps = area.Intersects(otherArea);
bool hasPositiveArea = area.IntersectsStrict(otherArea);

bool boxTouchesOrOverlaps = box.Intersects(otherBox);
bool hasPositiveVolume = box.IntersectsStrict(otherBox);

IntersectsStrict rejects boundary-only contact and zero-area or zero-volume inputs. Strict frustum overloads are not part of the public surface; frustum classification uses plane tests and should grow a separate contract only if a measured caller needs positive-volume frustum semantics.

Primitives

Segments preserve ordered endpoint identity:

FixedSegment segment = new(start3d, end3d);
Vector3d closest = segment.ClosestPoint(point3d);
Fixed64 distanceSquared = segment.DistanceSquared(point3d);
FixedBoundBox bounds = segment.Bounds;

Reversed endpoints produce the same bounds but are not equal. This keeps directed segment use cases deterministic without hiding identity policy inside the primitive.

Triangles also preserve ordered vertices:

FixedTriangle triangle = new(a3d, b3d, c3d);
Vector3d point = triangle.GetPoint(weightB, weightC);
bool inside = triangle.Contains(point);
Vector3d closest = triangle.ClosestPoint(point);

FixedTriangle2d.TryGetBarycentricWeights(...) solves planar barycentric weights directly. FixedTriangle.TryGetProjectedBarycentricWeights(...) names the 3D projection behavior explicitly so callers do not confuse projected weights with strict on-plane containment.