PolyhedralSurface

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What is a PolyhedralSurface?

A PolyhedralSurface is a surface assembled from flat Polygon patches joined along shared edges in three-dimensional space. It may be open; it does not by itself represent a solid.

Flatness and adjacency describe the intended surface geometry. Spatial Types stores patches without checking planarity, connectivity or surface topology. Construction does not certify a valid surface; use explicit geometric validation for the checks supported by your validator.

PolyhedralSurface — Supported representations

Availability in the current version of Spatial Types:

Coordinate layout	Geometry Mutable	Geometry Immutable	Geography Mutable	Geography Immutable
XY	❌	❌	❌	❌
XYZ	✅	✅	✅	✅
XYM	❌	❌	❌	❌
XYZM	✅	✅	✅	✅

In the current version, PolyhedralSurface is implemented only for layouts containing Z: XYZ and XYZM.

Creating the illustrated objects

The examples recreate the labelled objects above using Geometry in XYZ. Composer’s autoloader must already be loaded. Variable names match the point letters in the illustration.

Immutable objects

<?php

use LongitudeOne\SpatialTypes\Types\Dimension3z\Geometry\PointImmutable;
use LongitudeOne\SpatialTypes\Types\Dimension3z\Geometry\LineStringImmutable;
use LongitudeOne\SpatialTypes\Types\Dimension3z\Geometry\PolygonImmutable;
use LongitudeOne\SpatialTypes\Types\Dimension3z\Geometry\PolyhedralSurfaceImmutable;

// Immutable objects must be fully initialized through their constructors.

$a = new PointImmutable(-4, 0, 2);
$b = new PointImmutable(0, 0, 0);
$c = new PointImmutable(0, 6, 0);
$d = new PointImmutable(-4, 6, 2);
$e = new PointImmutable(4, 0, 2);
$f = new PointImmutable(4, 6, 2);
$g = new PointImmutable(0, 0, 0);
$h = new PointImmutable(4, 0, 0);
$i = new PointImmutable(4, 4, 0);
$j = new PointImmutable(0, 4, 0);
$k = new PointImmutable(2, 2, 3);

$leftRing = new LineStringImmutable([$a, $b, $c, $d, $a]);
$leftPatch = new PolygonImmutable([$leftRing]);
$rightRing = new LineStringImmutable([$b, $e, $f, $c, $b]);
$rightPatch = new PolygonImmutable([$rightRing]);
$openSurface = new PolyhedralSurfaceImmutable([$leftPatch, $rightPatch]);

$baseRing = new LineStringImmutable([$g, $j, $i, $h, $g]);
$basePatch = new PolygonImmutable([$baseRing]);
$sideRing1 = new LineStringImmutable([$g, $h, $k, $g]);
$sidePatch1 = new PolygonImmutable([$sideRing1]);
$sideRing2 = new LineStringImmutable([$h, $i, $k, $h]);
$sidePatch2 = new PolygonImmutable([$sideRing2]);
$sideRing3 = new LineStringImmutable([$i, $j, $k, $i]);
$sidePatch3 = new PolygonImmutable([$sideRing3]);
$sideRing4 = new LineStringImmutable([$j, $g, $k, $j]);
$sidePatch4 = new PolygonImmutable([$sideRing4]);
$pyramid = new PolyhedralSurfaceImmutable([
    $basePatch,
    $sidePatch1,
    $sidePatch2,
    $sidePatch3,
    $sidePatch4,
]);

Mutable objects

<?php

use LongitudeOne\SpatialTypes\Types\Dimension3z\Point;
use LongitudeOne\SpatialTypes\Types\Dimension3z\LineString;
use LongitudeOne\SpatialTypes\Types\Dimension3z\Polygon;
use LongitudeOne\SpatialTypes\Types\Dimension3z\PolyhedralSurface;

$a = new Point(-4, 0, 2);
$b = new Point(0, 0, 0);
$c = new Point(0, 6, 0);
$d = new Point(-4, 6, 2);
$e = new Point(4, 0, 2);
$f = new Point(4, 6, 2);
$g = new Point(0, 0, 0);
$h = new Point(4, 0, 0);
$i = new Point(4, 4, 0);
$j = new Point(0, 4, 0);
$k = new Point(2, 2, 3);

$leftRing = new LineString([$a, $b, $c, $d, $a]);
$leftPatch = new Polygon([$leftRing]);
$rightRing = new LineString([$b, $e, $f, $c, $b]);
$rightPatch = new Polygon([$rightRing]);
$openSurface = new PolyhedralSurface([$leftPatch, $rightPatch]); // Using the constructor.

$baseRing = new LineString([$g, $j, $i, $h, $g]);
$basePatch = new Polygon([$baseRing]);
$sideRing1 = new LineString([$g, $h, $k, $g]);
$sidePatch1 = new Polygon([$sideRing1]);
$sideRing2 = new LineString([$h, $i, $k, $h]);
$sidePatch2 = new Polygon([$sideRing2]);
$sideRing3 = new LineString([$i, $j, $k, $i]);
$sidePatch3 = new Polygon([$sideRing3]);
$sideRing4 = new LineString([$j, $g, $k, $j]);
$sidePatch4 = new Polygon([$sideRing4]);
// Starting empty and adding patches with methods.
$pyramid = new PolyhedralSurface()
    ->addPatch($basePatch)
    ->addPatch($sidePatch1)
    ->addPatch($sidePatch2)
    ->addPatch($sidePatch3)
    ->addPatch($sidePatch4);