Crate axiolid_hidden_lines 

Exact orthographic and perspective hidden-line drawings of triangle meshes (ADR 0090, 0107).

ScalarHiddenLines implements MeshHiddenLines. Visibility is decided exactly in the view’s affine frame: the image of a vertex is an exact polynomial of the binary64 inputs and the frame, every visibility question along an edge is an affine function of the edge parameter, and each sign is decided by the interval filter and, when that cannot decide, by dyadic big-integer arithmetic (axiolid-exact). Nothing is rounded before a decision; only the endpoints of the output pieces are, each the exact point rounded once to the nearest binary64. With EdgeSelection::group_boundary it also draws the edges between face groups, and FaceGroups::Planar derives the groups exactly (ADR 0106).

A perspective view (ADR 0107) is a pinhole at the frame origin: the image of (U, V, W) is (U / -W, V / -W). Every sign question is then an exact determinant of view-space vectors from the eye (recipe), affine in the edge parameter as before, so nothing divides before it is decided and a triangle behind the eye needs no case of its own (an edge-on triangle that contains the eye is decided exactly and its fibre starts at the eye, see occlusion); the endpoints are the exact rationals rounded once, and a near-plane cap is decided by ray parity along the eye ray (caps). The visible-face provider below is orthographic only. A vertex at or behind the eye plane (W >= 0) has no finite image, so a triangle beside or behind the eye makes the broad phase search the whole scene with the linear scan, as ScanHiddenLines does; the pairs, and so the drawing, are the same, and only the candidate search is slower.

ScalarVisibleFaces implements MeshVisibleFaces (ADR 0094) on the same view: the regions of the image where a face group (or the cap of a solid cut by the near plane) is frontmost. It cuts the image with an exact arrangement (axiolid-exact-arrangement) of the visible edge pieces, clip segments, cross-sections of interpenetrating triangles and the crop box, labels each side of each piece exactly, and snap-rounds the regions to the binary64 grid (ADR 0100): where no edge passes through the rounding cell of another vertex, each region vertex is the exact point rounded once and equals the hidden-line endpoint of the same point.

Module map: view (the affine map), recipe (the sign questions), param (parameters along an edge and their interval algebra), edges (topology and edge kinds), groups (face groups, planar ones derived), broad (candidate triangles from a BVH), occlusion (one edge against the triangles), caps (the cross-sections of solids a near plane cuts), output (correctly rounded endpoints), prepare (request validation and the scene shared with the visible-face operation), provider (the hidden-line provider itself), faces (the visible-face provider; its module docs give the algorithm).

Structs

ScalarHiddenLines

Portable exact hidden-line provider for orthographic and perspective views.

ScalarVisibleFaces

Portable exact orthographic visible-face provider.