*

Assets/Scripts/AdvancedMath.cs

@@ -0,0 +1,125 @@
+using UnityEngine;
+using System.Collections;
+using System.Collections.Generic;
+
+public static class AdvancedMath {
+
+	public static float TriangleSquare(Vector3 va, Vector3 vb, Vector3 vc){
+		float a = Vector3.Distance (va, vb);
+		float b = Vector3.Distance (vb, vc);
+		float c = Vector3.Distance (vc, va);
+		float p = (a + b + c) * 0.5f;
+		return Mathf.Sqrt (p * (p - a) * (p - b) * (p - c));
+	}
+
+
+
+	public static Vector3 PrismCenterOfMass(Vector3 v0, Vector3 v1, Vector3 v2, Vector3 normal, float h0, float h1, float h2){
+
+			
+		Vector3 a = v0 + normal * (h0 * 0.5f);
+		Vector3 c = v1 + normal * (h1 * 0.5f);
+		Vector3 b = v2 + normal * (h2 * 0.5f);
+		
+		Vector3 f = (a + b + c) / 3.0f;
+		
+		return (h0 * ((3.0f * f + a) / 4.0f) + h1 * ((3.0f * f + c) / 4.0f) + h2 * ((3.0f * f + b) / 4.0f)) / (h0 + h1 + h2);
+	}
+
+	public static float CylinderVolume(float r, float h){
+		return Mathf.PI * (r * r) * h;
+	}
+
+	public static Vector3 TriangleNormal(Vector3 va, Vector3 vb, Vector3 vc){
+		Vector3 ba = vb - va;
+		Vector3 ca = vc - va;
+		return Vector3.Cross(ba, ca).normalized;
+	}
+
+	public static Vector3 LineNearestPoint(Vector3 a, Vector3 b, Vector3 p){
+		Vector3 n = (b - a).normalized;
+		Vector3 pa = p - a;
+		float d = Vector3.Dot (n, pa);
+		return a + n * d;
+	}
+
+	public static float LineDistance(Vector3 a, Vector3 b, Vector3 p){
+		Vector3 lp = LineNearestPoint(a, b, p);
+		return Vector3.Distance (lp, p);
+	}
+
+	public static float Drag(float envDensity, float objVelocity, float dragCoeff, float referenceaArea){
+		return (envDensity * (objVelocity * objVelocity) * dragCoeff * referenceaArea) * 0.5f;
+	}
+
+	public static float SphereDrag(float envDensity, float objVelocity, float radius){
+		return Drag (envDensity, objVelocity, 0.47f, Mathf.PI * (radius * radius));
+	}
+
+	public static float BuoyantForce(float objectV, float objectDensity, float envDensity, float g){
+		return objectV * envDensity * g * ((3.0f * objectDensity) / (envDensity + 2.0f * objectDensity));
+	}
+	public static float SphereSegmentVolume(float r, float h){
+		return (Mathf.PI * (h * h) * (3.0f * r - h)) / 3.0f;
+	}
+	public static float SphereVolume(float r){
+		return (4.0f * Mathf.PI * (r * r * r)) / 3.0f;
+	}
+	public static float SphereSurfaceArea(float r){
+		return 4.0f * Mathf.PI * (r * r);
+	}
+	public static float PrismVolume(float baseArea, float h){
+		return baseArea * h;
+	}
+	public static float ConeVolume(float r, float h){
+		return (Mathf.PI * (r * r) * h) / 3.0f;
+	}
+	public static float PyramidVolume(float baseArea, float h){
+		return (baseArea * h) / 3.0f;
+	}
+	public static float RightTriangleArea(float a, float b){
+		return a * b * 0.5f;
+	}
+	public static float MeshVolume(Vector3[] srcVertices, int[] srcIndices, Matrix4x4 tf){
+		Vector3[] vertices = new Vector3[srcVertices.Length];
+		vertices[0] = tf.MultiplyPoint3x4(srcVertices[0]);
+		Vector3 vMin = vertices [0];
+		Vector3 vMax = vertices [0];
+		for (int i = 1; i < vertices.Length; ++i) {
+			vertices[i] = tf.MultiplyPoint3x4(srcVertices[i]);
+			vMin = Vector3.Min(vMin, vertices[i]);
+			vMax = Vector3.Max(vMax, vertices[i]);
+		}
+		
+		Plane p = new Plane (Vector3.up, vMax + Vector3.up);
+		
+		//split mesh by plane
+		List<Vector3> cuttedTriangles = AdvancedUtils.CutMesh (vertices, srcIndices, p);
+		
+		float totalVolume = 0.0f;
+		
+		for (int i = 0; i < cuttedTriangles.Count; i+=3) {
+			Vector3 v0 = cuttedTriangles[i + 0];
+			Vector3 v1 = cuttedTriangles[i + 1];
+			Vector3 v2 = cuttedTriangles[i + 2];
+			Vector3 normal = AdvancedMath.TriangleNormal(v0, v1, v2);
+			
+			float sign = Mathf.Sign(Vector3.Dot (normal, p.normal));
+			
+			float h0 = p.GetDistanceToPoint(v0);
+			float h1 = p.GetDistanceToPoint(v1);
+			float h2 = p.GetDistanceToPoint(v2);
+			float avgH = (h0 + h1 + h2) / 3.0f;
+			
+			Vector3 vp0 = v0 - p.normal * h0;
+			Vector3 vp1 = v1 - p.normal * h1;
+			Vector3 vp2 = v2 - p.normal * h2;
+			
+			float triangleSquare = AdvancedMath.TriangleSquare(vp0, vp1, vp2);
+			float prismVolume = AdvancedMath.PrismVolume(triangleSquare, avgH) * sign;
+			totalVolume += prismVolume;
+		}
+
+		return totalVolume;
+	}
+}