part of Unity.Library.eppz
- Polygon-Point containment
- Polygon-Segment intersection test
- Polygon permiter-Point containment (Precise)
- Polygon permiter-Point containment (Default)
- Polygon-Segment containment
- Polygon-Polygon containment
- Vertex facing
- Polygon area, Polygon winding
- Segment-Segment intersection point
- Polygon offset
- Multiple polygon centroid
- Polygon triangulation
These test scenes are designed to experience / proof the eppz! Geometry library features. Hit play, then manipulate the geometry in Scene window while in game mode (watch out to move the points directly instead their parent container). Every relevant code is in the corresponding Controller_#.cs, so you can see how to use the API.
You can define a polygon with simple Vector2[] array, but for sake of simplicity, test scenes uses some polygon sourcing helper classes (Components.PolygonSource) those take simple GameObject transforms as input. They also keep the polygon models updated on GameObject changes.
Another helper objects are polygon line renderers (Lines.PolygonLineRenderer). These renderers are DirectLineRenderer using fellow library eppz! Lines.
Beside these helper classes, you can easily construct Polygon / Segment instances using simple Vector2 inputs as well. Having these test scenes, you can easily provision the mechanism of each geometry feature even with your own polygons.
The star polygon drawn yellow when it contains all three points.
- When points appear to be on a polygon edge, test will return false
- When point is at a polygon vertex, test will return false
bool test = polygon.ContainsPoint(point);See Controller_0.cs for the full script context.
The star polygon drawn yellow when any of the two segments intersects any polygon edge.
- Returns false when a segment endpoint appears to be on a polygon edge
- Returns false when a segment endpoint is at a polygon vertex
bool test = polygon.IsIntersectingWithSegment(segment);See Controller_1.cs for the full script context.
The star polygon drawn yellow when the point is contained by the polygon permiter. Accuracy means the line width of the polygon permiter (is 1.0f by default).
- Returns true even if the point appears to be on a polygon edge
- Returns true even if the point is at a polygon vertex
bool test = polygon.PermiterContainsPoint(point, accuracy, Segment.ContainmentMethod.Precise);See Controller_2.cs for the full script context.
Points contained by a segment (even edge or polygon permiter) should be calculated with a given accuracy. This accuracy is set to 1e-6f by default, but can be set to any value per each containment test (like above).
Point containment tests has two containment method, ContainmentMethod.Default and ContainmentMethod.Precise. The former is less computation intensive than the latter. Depending on your ue case, you may trade precision over performance. The figure below summarizes the dissimilarities of the two method.
Actually the same as before, but a smaller accuracy is given (0.1f). The star polygon drawn yellow when the point appears to be on any polygon edge of at a polygon vertex.
- Returns true even if the point appears to be on a polygon edge
- Returns true even if the point is at a polygon vertex
float accuracy = 0.1f;
bool test = polygon.PermiterContainsPoint(point, accuracy);See Controller_3.cs for the full script context.
The star drawn yellow when it contains both edge. This is a compund test of polygon-point containment, polygon permiter-point containment, polygon-segment intersection.
- Returns true even if the point appears to be on a polygon edge (thanks to permiter test)
- Returns true even if the point is at a polygon vertex (thanks to permiter test)
See Controller_4.cs for the full script context.
The star drawn yellow when it contain the rectangular polygon. This is also a compund test of polygon-point containment, polygon-segment intersection, polygon permiter-point containment.
A polygon contains another polygon, when
- other polygon vertices are contained by polygon
- other polygon segments are not intersecting with polygon
- other polygon vertices are not contained by polygon permiter
See Controller_5.cs for the full script context.
The segments in ths example can think of imaginary polygon edges. The corner vertex normal segment drawn yellow when it faces inward the imaginary polygon, drawn white when facing outward.
It uses Segment.IsPointLeft() to create a compund test with both segments. It full calculation goes like below.
The two segments encompasses an acute angle if
- the endpoint of the second segment lies on the left of the first segment
The vertex normal facing outward if
- the neighbouring segment encompasses an acute angle
- and the normal point lies on the left of both segments
- or the neighbouring segments encompass an obtuse angle
- and the normal point lies on the left of one of the segments
See Controller_6.cs for the full script context.
The winding direction of a polygon comes to a good use when you want to validate the result of further polygon operations. The winding property of each Polygon instance gets calculated at construction time, and each time its topology gets updated (using UpdatePointPositionsWithSource(), UpdatePointPositionsWithTransforms(), Scale(), Translate()), or you can invoke Calculate() directly if you manipulated underlying point models directly.
In this scene you can see how area and winding of a polygon gets calculated. Just hit play and nudge some points around.
// After a polygon constructed, you can simply access values.
float area = polygon.area;
bool isCW = polygon.isCW;See Model/Polygon.cs source for the details.
Segment intersection has two parts actually. Get the intersection point of the lines defined by the segment, then look up if the point resides on the segments.
The first part has implemented as a generic Geometry.IntersectionOfSegments().
The second part gets more tricky, uses accuracy like many tests above. Checks if bounds are overlap, after that it uses the segment-point containment for the endpoints, then checks if the segments has intersection point at all (using winding tests), then returns with the intersection point of lines.
To avoid redundant test method calls, the method follows API style of
Physics.Raycast, where you can query if there is intersection at all, then use point only if any.
// Output will have non-zero value only on having a valid intersection.
Vector2 intersectionPoint;
bool isIntersecting = a.IntersectionWithSegment(b, out intersectionPoint);See Controller_8.cs for the full script context.
Robust polygon offset (also known as polygon outline / polygon buffer) solution (using Clipper by Angus Johnson).
float offset = 0.2f;
Polygon offsetPolygon = polygon.OffsetPolygon(offset);See Controller_9.cs for the full script context.
You can see how the compound centorid changes as you nudge polygons, vertices around. Algorithm uses Geometric decomposition.
// Calculate compund centroid.
centroid.position = Geometry.CentroidOfPolygons(polygons));See Controller_10.cs for the full script context.
This scene uses a Source.Mesh component to simply triangluate a polygon. If both Source.Polygon and UnityEngine.MeshFilter component is present on a GameObject, you can use this setup. It uses an extension method Polygon.Mesh() that hooks up Triangle.NET mesh output into a UnityEngine.MeshFilter (with some additional issue resolved regarding self intersecting polygons).
// Assign trianglated mesh.
meshFilter.mesh = polygon.Mesh(color, triangulator);See Source/Mesh.cs source for the details.
Licensed under the MIT License.