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C Sharp in Grasshopper | 点线面体操作大全

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    Jiaqi Wang(Ramis)
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[ 最后更新 于 2025-4-7 22:41 ]

鹅鹅打工速查手册

《3D打工人离不开的 点线面体的初始化 属性 和 方法合集》

点和向量

创建 Creating

Point3d pt1 = new Point3d(0, 0, 0);
Vector3d Vector = new Vector3d(5, 5, 0);

属性 Attribute

double x = pt1.X;
double y = pt1.Y;
double z = pt1.Z;

double x = v1.X;
double y = v1.Y;
double z = v1.Z;
double length = v1.Length;

方法和实用操作 Methods and Operations

显然，这里的操作均符合解析几何的设定：点和向量以及向量和向量之间可以做加法； 点和点相减获得向量；向量向量相乘获得点积；


Point3d pt3=pt1+moveVector;//点的移动
Vector3d v3=v2+v1;//向量叠加
Vector3d lineDirection=pt2-pt1;//点之间的向量
double dot=v1*v1;//向量点积

v1.Unitize();//获得单位向量

另外，垂直向量没有自带的方法，直接利用数学属性即可；求点到直线的垂点也是通过经典向量内积的定义来反推的：


Vector3d v = line1.Direction;
Vector3d d = z - line1.PointAt(0);
double t = (d*v) / (v * v);
Point3d projection_point = line1.PointAt(0) + t * v;
c=projection_point;

Vector3d perpVector = new Vector3d(-v1.Y, v1.X, 0);//取垂直向量

还有非常非常实用的 计算距离：因为 所有的线面距离问题最终基本最终都划归为找点。

double d1 = ps1.DistanceTo(ps2);

线 Line, Polyline, Interpolated and NurbsCurve

创建 Creating

最基础的两点成线 Line

Line line1 = new Line(pt1, pt2);

多段线/折线 Polyline

Polyline pl = new Polyline(pt_list); //注意此处如果需要polyline是closed，则第一个点和list里最后一个点需要重复

内插点曲线 Interpolated Curve

List<Point3d> pts = new List<Point3d>() { pt1, pt2, pt3 };
Curve crv = Curve.CreateInterpolatedCurve(pts, 3);

非均匀有理B样条曲线 NurbsCurve

（老天，我第一次知道这个东西中文名

注意 不同于其他曲线，这里多了一个Degree参数，用来设置阶数。一般默认就3吧

Curve crv = NurbsCurve.CreateControlPointCurve(x, 3);

注意 曲线折线之间可以相互转化，方便后续各种函数的调用（因为貌似很多函数都需要NurbsCurve）

Curve crv = line1.ToNurbsCurve();
NurbsCurve nc = crv as NurbsCurve;

方法和属性 Methods and Attribute

曲线端点

Interval domain = curve.Domain;
double t_start = domain.T0;  // Start of the curve domain
double t_end = domain.T1;    //End of the curve domain

曲线切分 Divide a Curve and Get Points

double[] parameters = x.ToNurbsCurve().DivideByCount(5, true);
Point3d[] dividePts = parameters.Select(t => x.PointAt(t)).ToArray();

曲线长度 Get Curve Length

double length = crv.GetLength(); //注意 这个函数对line无效

获取控制点 Extract Control Points from a Curve

注意这里的控制点 不只是点 点的location才是点本身（好绕…

List<Point3d> controlPts = new List<Point3d>();
foreach (ControlPoint pt in crva.Points)
{
    controlPts.Add(pt.Location);
}

Example: Creating a Grid with Polylines

int u = 6; // Number of rows
int v = 10; // Number of columns

List<Polyline> pylList = new List<Polyline>();

// Generate row polylines
for (int i = 0; i < u; i++)
{
    List<Point3d> ptList = new List<Point3d>();
    for (int j = 0; j < v; j++)
    {
        int id = j * u + i;
        ptList.Add(x[id]);
    }
    pylList.Add(new Polyline(ptList));
}

// Generate column polylines
for (int i = 0; i < v; i++)
{
    List<Point3d> ptList = new List<Point3d>();
    for (int j = 0; j < u; j++)
    {
        int idx = j + i * u;
        ptList.Add(x[idx]);
    }
    pylList.Add(new Polyline(ptList));
}

a = pylList;

面 Surface

创建 Creating

通过角点来创建：Creating a Surface from Corner Points

NurbsSurface srf = NurbsSurface.CreateFromCorners(pt1, pt2, pt3);// 三点的平面
NurbsSurface srf = NurbsSurface.CreateFromCorners(pt1, pt2, pt3, pt4);// 四点的曲面

通过多个点创建曲面：Creating a NurbsSurface from Multiple Points

NurbsSurface nrb = NurbsSurface.CreateFromPoints(pt1, pt2, pt3, pt4, pt5);

通过封闭曲线创建平面 Creating a Surface from a Closed Curve

Brep[] b = Brep.CreatePlanarBreps(x, 0.001);
surface=b[0];

创建曲线的骨架平面 Creating Curve frame Plane

Interval dd=crv.Domain;
List<Plane> planes = new List<Plane>();
for (int i=0;i<n;i++)
{
Plane currentPlane;
crv.PerpendicularFrameAt(((domain.T1-domain.T0)/n*i), out currentPlane);
planes.Add(currentPlane);
}

实例：创建简单长方形平面:

Polyline rec = new Polyline(new List<Point3d> { pt1, pt2, pt3, pt4, pt1 });
Curve recCurve = rec.ToNurbsCurve();

// Create a planar Brep from the curve
Brep[] breps = Brep.CreatePlanarBreps(recCurve, 0.001);
if (breps != null && breps.Length > 0)
{
    Brep br = breps[0];
    Surface srf = br.Surfaces[0];
}

（已经翻译不好了 以下几个放弃翻译）

Creating a Surface by Extruding a Curve

// Define a curve x and an extrusion direction y
Surface srf1 = Surface.CreateExtrusion(x, y);

Creating a Surface from Multiple Curves

注意如果多个线相互包含 会处理面上有洞洞的情况！

List<Curve> crvs = new List<Curve> { x, y };
Brep[] b = Brep.CreatePlanarBreps(crvs, 0.001);

Creating a Surface from Loft

Brep[] b = Brep.CreateFromLoft(x, Point3d.Unset, Point3d.Unset, LoftType.Normal, false);

Creating a Surface from Sweep

Brep[] sweptBreps = Brep.CreateFromSweep(x, y, true, 0.01);

方法 Methods

获得控制点 Getting Control Points of a Surface

NurbsSurface srf = x.ToNurbsSurface();
var cpts = srf.Points;
List<Point3d> pts = new List<Point3d>();

foreach (ControlPoint cpt in cpts)
{
    pts.Add(cpt.Location);
}
a = pts;

用经纬重新切分曲面 Subdividing a Surface and Getting Points at (u, v) Coordinates

这个地方细说一下，uv是把面分为从0到1，但是每个曲面自带的经纬编号不一定是从零到1，所以需要引入一个interval把经纬两轴确定一下长度（此处是一个相对长度，可以看作是有几个经度几个纬度）然后重新参数化。之后我们再根据从0到1的相对位置找点。

// Get domain intervals in U and V directions
Interval i1 = x.Domain(0);
Interval i2 = x.Domain(1);

// Map (u, v) between (0,1) to the actual surface domain
double uu = i1.ParameterAt(u);
double vv = i2.ParameterAt(v);

// Get the point on the surface
Point3d pt = x.PointAt(uu, vv);

计算曲线面积 Surface Area Calculation

double ar = AreaMassProperties.Compute(srf).Area;//对封闭曲线据说也可行

体 Brep（Boundary representation）

创建

BOX


Interval x = new Interval(-2, 2);
Interval y = new Interval(-10, 10);
Interval z = new Interval(-5, 5);

// Step 2: Create box using intervals
Box box = new Box(Plane.WorldXY, x, y, z);

// Step 3: Convert box to brep
Brep brep = box.ToBrep();

Join brep


    Brep[] closedBrep = Brep.JoinBreps(allBreps, RhinoDoc.ActiveDoc.ModelAbsoluteTolerance);
Cat

非常高产又有趣的星期三。我居然还能22：40写这个小笔记。老天。 啊啊啊啊拥有一个ENTJ老板真的是让我又爱又恨。INTP弱小ing。

-鹅仔 2025/03/12 22：39

2025/04/07 21：09 更新了 体量的相关操作以及其他关于curve的补充 还有一些常用的属性更新

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