102 lines
3.9 KiB
C#
102 lines
3.9 KiB
C#
using UnityEngine;
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namespace BrainFailProductions.PolyFew.AsImpL.MathUtil
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{
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/// <summary>
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/// Collection of useful mathematical methods.
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/// </summary>
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public static class MathUtility
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{
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/// <summary>
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/// Clamp list indices.
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/// </summary>
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/// <param name="index">Index to be clamped.</param>
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/// <param name="listSize">Size of the list.</param>
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/// <returns></returns>
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/// <remarks>
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/// Will even work if index is larger/smaller than listSize, so can loop multiple times
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/// From https://www.habrador.com/tutorials/math/9-useful-algorithms/
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/// </remarks>
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public static int ClampListIndex(int index, int listSize)
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{
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index = ((index % listSize) + listSize) % listSize;
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return index;
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}
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//p is the testpoint, and the other points are corners in the triangle
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/// <summary>
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/// Check if a point is inside a triangle.
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/// </summary>
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/// <param name="p1">First corner in the triangle.</param>
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/// <param name="p2">Second corner in the triangle.</param>
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/// <param name="p3">Third corner in the triangle.</param>
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/// <param name="p">Test point</param>
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/// <returns>The result is true if the test point is inside the triangle.</returns>
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/// <remarks>
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/// From https://www.habrador.com/tutorials/math/9-useful-algorithms/
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/// http://totologic.blogspot.se/2014/01/accurate-point-in-triangle-test.html
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/// </remarks>
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public static bool IsPointInTriangle(Vector2 p1, Vector2 p2, Vector2 p3, Vector2 p)
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{
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bool isWithinTriangle = false;
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//Based on Barycentric coordinates
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float denominator = ((p2.y - p3.y) * (p1.x - p3.x) + (p3.x - p2.x) * (p1.y - p3.y));
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float a = ((p2.y - p3.y) * (p.x - p3.x) + (p3.x - p2.x) * (p.y - p3.y)) / denominator;
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float b = ((p3.y - p1.y) * (p.x - p3.x) + (p1.x - p3.x) * (p.y - p3.y)) / denominator;
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float c = 1 - a - b;
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//The point is within the triangle
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if (a > 0f && a < 1f && b > 0f && b < 1f && c > 0f && c < 1f)
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{
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isWithinTriangle = true;
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}
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return isWithinTriangle;
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}
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/// <summary>
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/// Check if a triangle oriented clockwise or counter-clockwise.
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/// </summary>
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/// <param name="v1">First vectex in 2D</param>
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/// <param name="v2">Second vectex in 2D</param>
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/// <param name="v3">Third vectex in 2D</param>
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/// <returns>True if the triangle is oriented clockwise.</returns>
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/// <remarks>
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/// This comes from:
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/// https://www.habrador.com/tutorials/math/9-useful-algorithms/
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/// https://math.stackexchange.com/questions/1324179/how-to-tell-if-3-connected-points-are-connected-clockwise-or-counter-clockwise
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/// https://en.wikipedia.org/wiki/Curve_orientation
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/// </remarks>
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public static bool IsTriangleOrientedClockwise(Vector2 v1, Vector2 v2, Vector2 v3)
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{
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float determinant = v1.x * v2.y + v3.x * v1.y + v2.x * v3.y - v1.x * v3.y - v3.x * v2.y - v2.x * v1.y;
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bool isClockWise = determinant > 0f;
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return isClockWise;
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}
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/// <summary>
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/// Compute the normal of a vertex of a triangle defined by its 3 vertices.
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/// </summary>
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/// <param name="vert">Vertex of the triangle where the normal is coputed.</param>
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/// <param name="vNext">Next vertex (counter-clockwise)</param>
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/// <param name="vPrev">Previous vertex (counter-clockwise)</param>
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/// <returns>The computed normal.</returns>
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public static Vector3 ComputeNormal(Vector3 vert, Vector3 vNext, Vector3 vPrev)
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{
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Vector3 n = Vector3.Cross(vPrev - vert, vNext - vert);
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n.Normalize();
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return n;
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}
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}
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}
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