/// <summary>
/// 求被分割一部分的圆柱体表面每一圈的点
/// </summary>
/// <param name="divisionNumber">一圈的三角形的个数</param>
/// <param name="surplsAngle">被切后圆截面所剩的角度</param>
/// <param name="unitVectorU">下底圆所在平面上一个向量U</param>
/// <param name="unitVectorV">下底圆所在平面上一个向量与U垂足的向量V</param>
/// <returns></returns>
private List <List <Point> > GetSurfaceDivisionTrianglePoints(int divisionNumber, double surplsAngle, SpectVector unitVectorU, SpectVector unitVectorV)
{
List <List <Point> > divisionTrianglePoints = new List <List <Point> >();
RayInfo ZVectorRay = new RayInfo(this.bottomCirclePoint, this.topCirclePoint);
double H = this.topCirclePoint.GetDistance(this.bottomCirclePoint);
double L = surplsAngle / 360 * 2 * Math.PI * this.radius;
double a = L / divisionNumber;
double h = Math.Sqrt(3) * a / 2;
int j = 0;
double sumd = 0;
double beta = (surplsAngle * Math.PI / 180) / (2 * divisionNumber);
bool flag = true;
Point currentCenterPoint;
while (flag)
{
if (sumd < H)
{
currentCenterPoint = ZVectorRay.GetPointOnRayVector(j * h);
}
else
{
flag = false;
currentCenterPoint = this.topCirclePoint;
}
List <Point> circlePoints = new List <Point>();
//第一个点
circlePoints.Add(this.GetPointInCircumference(currentCenterPoint, this.radius, unitVectorU, unitVectorV, 0.01));
int i = 1;
if (j % 2 == 0)//处于偶数层时
{
while (i < divisionNumber)
{
circlePoints.Add(this.GetPointInCircumference(currentCenterPoint, this.radius, unitVectorU, unitVectorV, 2 * i * beta));
i++;
}
}
else//处于奇数层，奇数层要比偶数层多一个点
{
while (i <= divisionNumber)
{
circlePoints.Add(this.GetPointInCircumference(currentCenterPoint, this.radius, unitVectorU, unitVectorV, (2 * i - 1) * beta));
i++;
}
}
//最后一个点
circlePoints.Add(this.GetPointInCircumference(currentCenterPoint, this.radius, unitVectorU, unitVectorV, surplsAngle * Math.PI / 180 - 0.01));
divisionTrianglePoints.Add(circlePoints);
j++;
sumd += h;
}
return(divisionTrianglePoints);
}
/// <summary>
/// 求被分割一部分的圆台体表面的三角面单元
/// </summary>
/// <param name="divisionNumber">圆弧角的细分次数</param>
/// <param name="surplsAngle">下底面所剩部分的角度</param>
/// <param name="unitVectorU">下底圆所在平面上一个向量U</param>
/// <param name="unitVectorV">下底圆所在平面上一个向量与U垂足的向量V</param>
/// <returns></returns>
public List <List <Triangle> > GetTruncatedSurfaceDivisionTriangles(int divisionNumber, double surplsAngle, SpectVector unitVectorU, SpectVector unitVectorV)
{
//参考论文：基本体素的三角形面单元剖分方法
List <List <Triangle> > divisinTriangles = new List <List <Triangle> >();
RayInfo circleCenterPointsRay = new RayInfo(this.bottomCenterPoint, this.topCenterPoint);
double h = this.bottomCenterPoint.GetDistance(this.topCenterPoint);//圆台体的高
double l = Math.Sqrt((h * h + Math.Pow(this.bottomCircleRadius - this.topCircleRadius, 2)));
double L = this.bottomCircleRadius * l / (this.bottomCircleRadius - this.topCircleRadius);
double sinB = h / l;
double theta = 2 * Math.PI * this.bottomCircleRadius / L;//弧度制
double particalTheta = surplsAngle / 360 * theta;
int j = 0;
bool flag = true;
double alpha = particalTheta / divisionNumber;
double triangleSideLength = 2 * L * Math.Sin(alpha / 2);//正三角形初始边长
double d = Math.Sqrt(3) * triangleSideLength / 2 + L - L * Math.Cos(alpha / 2);
double beta = (surplsAngle * Math.PI / 180) / (2 * divisionNumber - 1);
double L1 = L;
double sumd = d;
double r1 = L1 * theta / (2 * Math.PI);// 弧长除以2*PI
Point currentCenterPoint = this.bottomCenterPoint;
while (flag)
{
double L2, r2, i = 0;
Point nextCenterPoint;
if (sumd < l)
{
L2 = L1 - d;
nextCenterPoint = circleCenterPointsRay.GetPointOnRayVector(sumd * sinB);
}
else
{
L2 = L - l;
flag = false;
nextCenterPoint = this.topCenterPoint;
}
r2 = L2 * theta / (2 * Math.PI);
double k = 1, r3;
Point tempPoint;
if (j % 2 == 0)//r1和r2交换
{
r3 = r1;
r1 = r2;
r2 = r3;
k = -1;
tempPoint = currentCenterPoint;
currentCenterPoint = nextCenterPoint;
nextCenterPoint = tempPoint;
}
List <Triangle> oneCircleTriangles = new List <Triangle>();
while (i < 2 * divisionNumber)
{
Point vertex1 = new Point(), vertex2 = new Point(), vertex3 = new Point(); //三角面的三个点
vertex1 = GetPointInCircumference(nextCenterPoint, r2, unitVectorU, unitVectorV, i * beta);
if (j % 2 == 1 && i == 0) //在单数的开始边界时
{
vertex2 = GetPointInCircumference(currentCenterPoint, r1, unitVectorU, unitVectorV, i * beta + 0.01);
}
else if (j % 2 == 1 && i == 2 * divisionNumber - 1)//在单数的结束边界时
{
vertex2 = GetPointInCircumference(currentCenterPoint, r1, unitVectorU, unitVectorV, i * beta - 0.01);
}
else
{
vertex2 = GetPointInCircumference(currentCenterPoint, r1, unitVectorU, unitVectorV, (i - k) * beta);
}
if (j % 2 == 0 && i == 0) //在双数开始边界时
{
vertex3 = GetPointInCircumference(currentCenterPoint, r1, unitVectorU, unitVectorV, i * beta + 0.01);
}
else if (j % 2 == 0 && i == 2 * divisionNumber - 1)//在双数结束边界时
{
vertex3 = GetPointInCircumference(currentCenterPoint, r1, unitVectorU, unitVectorV, i * beta - 0.01);
}
else
{
vertex3 = GetPointInCircumference(currentCenterPoint, r1, unitVectorU, unitVectorV, (i + k) * beta);
}
oneCircleTriangles.Add(new Triangle(vertex1, vertex2, vertex3));
r3 = r1;
r1 = r2;
r2 = r3;
k = -k;
tempPoint = currentCenterPoint;
currentCenterPoint = nextCenterPoint;
nextCenterPoint = tempPoint;
i++;
}
divisinTriangles.Add(oneCircleTriangles);
//
if (this.bottomCenterPoint.GetDistance(currentCenterPoint) < this.bottomCenterPoint.GetDistance(nextCenterPoint))
{
currentCenterPoint = nextCenterPoint;
}
L1 = Math.Min(L1, L2);
r1 = L1 * theta / (Math.PI * 2);
triangleSideLength = 2 * L1 * Math.Sin(alpha / 2);
d = Math.Sqrt(3) * triangleSideLength / 2 + L1 - L1 * Math.Cos(alpha / 2);
sumd += d;
j++;
}
return(divisinTriangles);
}
public Point GetCrossPointWithRay(RayInfo oneRay)
{
double high = this.bottomCirclePoint.GetDistance(this.topCirclePoint);
List <Point> crossPoints = this.Intersect(this.bottomCirclePoint, this.topCirclePoint, this.radius, high, oneRay.Origin, oneRay.GetPointOnRayVector(1));
if (crossPoints.Count == 1)
{
return(crossPoints[0]);
}
if (crossPoints.Count > 1)
{
Point nearestPoint = crossPoints[0];
for (int j = 1; j < crossPoints.Count; j++)
{
if (nearestPoint.GetDistance(oneRay.Origin) > crossPoints[j].GetDistance(oneRay.Origin))
{
nearestPoint = crossPoints[j];
}
}
return(nearestPoint);
}
return(null);
}
/// <summary>
/// 求被分割一部分的圆台体表面每个分割圆上的点
/// </summary>
/// <param name="divisionNumber">圆弧角的细分次数</param>
/// <param name="surplsAngle">下底面所剩部分的角度</param>
/// <param name="unitVectorU">下底圆所在平面上一个向量U</param>
/// <param name="unitVectorV">下底圆所在平面上一个向量与U垂足的向量V</param>
/// <returns></returns>
private List <List <Point> > GetConeSurfaceDivisionTrianglePoints(int divisionNumber, double surplsAngle, SpectVector unitVectorU, SpectVector unitVectorV)
{
//参考论文：基本体素的三角形面单元剖分方法-李鸿亮
//现在每个圆上取点，再组成三角面
List <List <Point> > divisionTrianglePoints = new List <List <Point> >();
RayInfo circleCenterPointsRay = new RayInfo(this.bottomCenterPoint, this.topCenterPoint);
double h = this.bottomCenterPoint.GetDistance(this.topCenterPoint);//圆台体的高
double l = Math.Sqrt((h * h + Math.Pow(this.bottomCircleRadius - this.topCircleRadius, 2)));
double L = this.bottomCircleRadius * l / (this.bottomCircleRadius - this.topCircleRadius);
double sinB = h / l;
double theta = 2 * Math.PI * this.bottomCircleRadius / L;//弧度制
double particalTheta = surplsAngle / 360 * theta;
int j = 0;
int I = 2 * divisionNumber + 1;
bool flag = true;
double alpha = particalTheta / divisionNumber;
double triangleSideLength = 2 * L * Math.Sin(alpha / 2);//正三角形初始边长
double d = Math.Sqrt(3) * triangleSideLength / 2 + L - L * Math.Cos(alpha / 2);
double beta = (surplsAngle * Math.PI / 180) / (2 * divisionNumber);
double currentL = L;
double sumd = 0;
double r = currentL * theta / (2 * Math.PI);// 弧长除以2*PI
while (flag)
{
Point currentCenterPoint;
if (sumd < l)
{
currentCenterPoint = circleCenterPointsRay.GetPointOnRayVector(sumd * sinB);
}
else
{
flag = false;
currentCenterPoint = this.topCenterPoint;
}
List <Point> circlePoints = new List <Point>();
int i = 1;
//第一个点
circlePoints.Add(this.GetPointInCircumference(currentCenterPoint, r, unitVectorU, unitVectorV, 0.01));
if (j % 2 == 0)//处于偶数层时
{
while (i < divisionNumber)
{
circlePoints.Add(this.GetPointInCircumference(currentCenterPoint, r, unitVectorU, unitVectorV, 2 * i * beta));
i++;
}
}
else//处于奇数层，奇数层要比偶数层多一个点
{
while (i <= divisionNumber)
{
circlePoints.Add(this.GetPointInCircumference(currentCenterPoint, r, unitVectorU, unitVectorV, (2 * i - 1) * beta));
i++;
}
}
//最后一个点
circlePoints.Add(this.GetPointInCircumference(currentCenterPoint, r, unitVectorU, unitVectorV, surplsAngle * Math.PI / 180 - 0.01));
divisionTrianglePoints.Add(circlePoints);
//
sumd += d;
currentL = currentL - d;
r = currentL * theta / (Math.PI * 2);
triangleSideLength = 2 * currentL * Math.Sin(alpha / 2);
d = Math.Sqrt(3) * triangleSideLength / 2 + currentL - currentL * Math.Cos(alpha / 2);
// sumd += d;
j++;
}
return(divisionTrianglePoints);
}