# Geometric Primitives

### CoordinateSystem

While Dynamo is capable of creating a variety of complex geometric forms, simple geometric primitives form the backbone of any computational design: either directly expressed in the final designed form, or used as scaffolding off of which more complex geometry is generated.

While not strictly a piece of geometry, the CoordinateSystem is an important tool for constructing geometry. A CoordinateSystem object keeps track of both position and geometric transformations such as rotation, sheer, and scaling.

Creating a CoordinateSystem centered at a point with x = 0, y = 0, z = 0, with no rotations, scaling, or sheering transformations, simply requires calling the Identity constructor:

![](https://1734247194-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FY5ZuHF3yuXFWp1C46ZSo%2Fuploads%2Fgit-blob-5ca4fd077f626d07bc9223187239ce35ff686974%2FGeometricPrimitives_01.png?alt=media\&token=65ff97d0-468b-45e1-ab02-62574edb8f27)

```js
// create a CoordinateSystem at x = 0, y = 0, z = 0,
// no rotations, scaling, or sheering transformations

cs = CoordinateSystem.Identity();
```

CoordinateSystems with geometric transformations are beyond the scope of this chapter, though another constructor allows you to create a coordinate system at a specific point, *CoordinateSystem.ByOriginVectors*:

![](https://1734247194-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FY5ZuHF3yuXFWp1C46ZSo%2Fuploads%2Fgit-blob-384862fe6f59087aabd28e55ea7cb3eb8e9a9aec%2FGeometricPrimitives_02.png?alt=media\&token=b726b136-2770-4ade-80ee-67b59aeafc5f)

```js
// create a CoordinateSystem at a specific location,
// no rotations, scaling, or sheering transformations
x_pos = 3.6;
y_pos = 9.4;
z_pos = 13.0;

origin = Point.ByCoordinates(x_pos, y_pos, z_pos);
identity = CoordinateSystem.Identity();

cs = CoordinateSystem.ByOriginVectors(origin,
    identity.XAxis, identity.YAxis, identity.ZAxis);
```

### Point

The simplest geometric primitive is a Point, representing a zero-dimensional location in three-dimensional space. As mentioned earlier there are several different ways to create a point in a particular coordinate system: *Point.ByCoordinates* creates a point with specified x, y, and z coordinates; *Point.ByCartesianCoordinates* creates a point with a specified x, y, and z coordinates in a specific coordinate system; *Point.ByCylindricalCoordinates* creates a point lying on a cylinder with radius, rotation angle, and height; and *Point.BySphericalCoordinates* creates a point lying on a sphere with radius and two rotation angle.

This example shows points created at various coordinate systems:

![](https://1734247194-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FY5ZuHF3yuXFWp1C46ZSo%2Fuploads%2Fgit-blob-580811d9b6d6b188fdedc7d7660ade6ddeec7d46%2FGeometricPrimitives_03.png?alt=media\&token=c42fe1a0-34ab-44a1-a846-283eb19f6f3b)

```js
// create a point with x, y, and z coordinates
x_pos = 1;
y_pos = 2;
z_pos = 3;

pCoord = Point.ByCoordinates(x_pos, y_pos, z_pos);

// create a point in a specific coordinate system
cs = CoordinateSystem.Identity();
pCoordSystem = Point.ByCartesianCoordinates(cs, x_pos,
    y_pos, z_pos);

// create a point on a cylinder with the following
// radius and height
radius = 5;
height = 15;
theta = 75.5;

pCyl = Point.ByCylindricalCoordinates(cs, radius, theta,
    height);

// create a point on a sphere with radius and two angles

phi = 120.3;

pSphere = Point.BySphericalCoordinates(cs, radius,
    theta, phi);
```

### Line

The next higher dimensional Dynamo primitive is a line segment, representing an infinite number of points between two end points. Lines can be created by explicitly stating the two boundary points with the constructor *Line.ByStartPointEndPoint*, or by specifying a start point, direction, and length in that direction, *Line.ByStartPointDirectionLength*.

![](https://1734247194-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FY5ZuHF3yuXFWp1C46ZSo%2Fuploads%2Fgit-blob-b7d66b948127e65b6df64015d4a2b9bd992c832f%2FGeometricPrimitives_04.png?alt=media\&token=5c5cb66a-83b4-42bb-88b8-51001ff7f0cf)

```js
p1 = Point.ByCoordinates(-2, -5, -10);
p2 = Point.ByCoordinates(6, 8, 10);

// a line segment between two points
l2pts = Line.ByStartPointEndPoint(p1, p2);

// a line segment at p1 in direction 1, 1, 1 with
// length 10
lDir = Line.ByStartPointDirectionLength(p1,
    Vector.ByCoordinates(1, 1, 1), 10);
```

### 3D Primitives - Cuboid, Cone, Cylinder, Sphere, etc

Dynamo has objects representing the most basic types of geometric primitives in three dimensions: Cuboids, created with *Cuboid.ByLengths*; Cones, created with *Cone.ByPointsRadius* and *Cone.ByPointsRadii*; Cylinders, created with *Cylinder.ByRadiusHeight*; and Spheres, created with *Sphere.ByCenterPointRadius*.

![](https://1734247194-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FY5ZuHF3yuXFWp1C46ZSo%2Fuploads%2Fgit-blob-2c3868829aff998b0ac130debb5c9252ed88c945%2FGeometricPrimitives_05.png?alt=media\&token=ec777a5d-7c53-464e-8e45-e9499ee2e54d)

```js
// create a cuboid with specified lengths
cs = CoordinateSystem.Identity();

cub = Cuboid.ByLengths(cs, 5, 15, 2);

// create several cones
p1 = Point.ByCoordinates(0, 0, 10);
p2 = Point.ByCoordinates(0, 0, 20);
p3 = Point.ByCoordinates(0, 0, 30);

cone1 = Cone.ByPointsRadii(p1, p2, 10, 6);
cone2 = Cone.ByPointsRadii(p2, p3, 6, 0);

// make a cylinder
cylCS = cs.Translate(10, 0, 0);

cyl = Cylinder.ByRadiusHeight(cylCS, 3, 10);

// make a sphere
centerP = Point.ByCoordinates(-10, -10, 0);

sph = Sphere.ByCenterPointRadius(centerP, 5);
```