E4 · Publication Volume 26

Raster, Vector, Point Cloud, Mesh, Voxel and 3D Computing

Builds robust spatial computing across vectors, rasters, point clouds, meshes, solids, voxels and block models.

Purpose and boundary of this book

This book develops reproducible spatial-computing methods across vector geometry, rasters, point clouds, polygon meshes, closed solids, voxels and block models. It explains representation choice, coordinate precision, topology, indexing, intersection, simplification, delivery formats and robust testing as one controlled evidence chain. It is a scientific methods tutorial, not a product manual.

This is a general, institution-neutral tutorial with no relationship to any company or individual. All coordinates, geometries, grids, points, surfaces, volumes, attributes and review events in the lesson are synthetic and must not be used for an operational decision.

The website carrying the material acts only as a host. It is not the owner, publisher, scientific authority or subject of the curriculum. Named standards and technical works appear in source sections to identify evidence used in preparing the tutorial.

One phenomenon, several representations

A geological boundary may be stored as a polyline, raster class transition, point-cloud classification, triangle mesh, closed solid or voxel label. These are not interchangeable pictures of the same thing. Each representation defines support, topology, interpolation, error and permitted operations. Conversion adds assumptions and usually loses information.

The central discipline is to state what the source asserts, what the target representation can express, which transformation is used, and which properties must be conserved. A fast renderable derivative never replaces the authoritative observation or interpretation from which it was made.

Learning outcomes

  • declare coordinate, precision, support and topology contracts for spatial objects;
  • validate and repair vector geometry without hiding changed meaning;
  • construct aligned raster grids and choose purpose-appropriate resampling;
  • design broad-phase indexes followed by exact spatial predicates;
  • interpret point density, classification, scale and level of detail;
  • validate mesh manifoldness, orientation, self-intersection and closure;
  • model solids, voxels and block models with explicit inside, support and transforms;
  • compute intersections and sections while handling tangency and degeneracy;
  • simplify and stream representations under measured error bounds; and
  • build golden, property and metamorphic tests for numerically robust spatial software.

Prerequisites, notation and conventions

The tutorial assumes the quantitative foundations of A1, three-dimensional geological reasoning from A4 and coordinate-reference principles from E1. E2 and E3 provide useful semantics, provenance and drillhole context; D1 provides geological-model context. No particular programming language, database, graphics engine or commercial software is required.

Coordinates are written as mathbf{x}=(x,y,z) in a declared right-handed frame. Raster integer indices are (i,j,k) and world coordinates are obtained through an explicit transform. Intervals and array extents use declared boundary conventions. Distances, areas and volumes always carry units. Tolerances are quantity-specific policies, not universal constants.

Synthetic teaching package

All exercises use an invented package named SYN-SPATIAL with local coordinates, a synthetic terrain raster, fabricated linework, a sampled point cloud, two surfaces, one closed test solid and a small rotated block model. The package deliberately contains duplicate vertices, near-collinear points, a bow-tie polygon, raster misalignment, sparse point regions, non-manifold edges, reversed faces, coplanar intersections and coordinates large enough to expose precision loss.

Every correction creates a derivative and keeps the received object. The package contains exact analytic fixtures beside approximate sampled representations so that learners can distinguish algorithm error from source uncertainty. Nothing in the package describes a real place, person, organisation, project or asset.

Representation decision record

Before processing, write a decision record containing intended questions, required dimensions, support, topology, accuracy, update frequency, size, query pattern, rendering need, interchange boundary and failure consequence. Then select the simplest representation that preserves the required evidence. Choosing a format before defining these requirements reverses the reasoning order.

The record also states which object is authoritative, which derivatives are reproducible, which are disposable delivery artefacts and which transformations are reversible only within a measured tolerance. Multiple derivatives may be valid for different tasks without any one becoming a universal master.

Evidence architecture and quality gates

Source evidence preserves received coordinates, attributes, files and acquisition or modelling context. Semantic evidence declares identity, coordinate reference, units, support, topology and value states. Process evidence records transform, index, predicate, interpolation, simplification and encoding. Decision evidence records findings, review, exceptions and release scope.

  • Required coordinate, unit, support and topology declarations resolve.
  • Every derivative identifies exact inputs, algorithm, parameters and numerical policy.
  • Representation-specific invariants pass before dependent operations run.
  • Measured error and uncertainty remain distinct from display resolution.
  • Unresolved hard failures block only the affected derivative and remain explainable.

Assessment and completion standard

The final assessed package contains a precision contract, vector-validity report, aligned raster pair, resampling comparison, spatial-index benchmark, point-cloud density and hierarchy report, mesh-quality report, closed-solid test, voxel or block-model transform, intersection fixtures, level-of-detail error table, delivery manifest and numerical regression suite.

Acceptance requires deterministic reruns, exact lineage, stable ordering, explicit tolerance and boundary policies, preserved attributes and support, no silent repair, measured conversion error and an explainable result for every failed predicate. A precise blocked result is valid; a visually plausible result produced by guessing metadata is not.

Core sources