**Method 3: Divide Surface + 5 Points Adaptive Component**

**The Strategy**

If I can create a ring surface with pattern of triangles arrayed radially, using the 5 points adaptive component as in Method 2C adapting to the points of the triangle, the center point and another point above the center, I can place one leg at a point. Again with repeater, the star is made.

**The Surface**

Attempt 1: Extrusion

- Create a solid surface with the outter circle and a volid with the inner circle to make a ring surface.
- Divide the surface with triangle (flat).
- Pattern of triangles is orthogonal, not radial. Fail.

Attempt 2: Sweep

- Draw a rectangle (reference lines) at the vertical plane (ZX plane) at the rim of the inner circle, select the rectangle and the inner circle, create a ring form.
- Select top ring surface, divide surface with triangle (flat).
- Pattern of triangles is orthogonal, not radial. Fail.

Attempt 3: Revolve

- Draw a reference line at the vertical plane (ZX plane) at the rim of the inner and outter circles, draw a vertical reference line at the vertical plane (ZX plane) at the center. Select both lines and create a ring form.
- Select the ring surface, divide surface with triangle (flat).
- Pattern of triangles is orthogonal, not radial. Fail.
- Select the point at the rim of the outter circle, move it up.
- Pattern of triangles is radial. However the surface is sloping, not flat. The nodes at the vertice of the triangles need to lie on a flat plane. Fail.

Attempt 4: Revolve with curved surface

To create a radial pattern of triangles, the surface cannot be flat. However it can be curved with the end points of the curve being at the same level.

- Draw a reference line at the vertical plane (ZX plane) at the rim of the inner and outter circles.
- Place a point at the midpoint of the reference line.
- Select the XY plane of the reference point, place another point on it.
- Move the new point down by giving it a negative offset value.
- Select the points at the rim of the inner and outter circles and the moved down point, create a spline through points, make the spline a reference line.
- Draw a vertical reference line at the vertical plane (ZX plane) at the center. Select the vertical line and the spline, create a ring form.
- Select the ring surface, divide surface with triangle (flat).
- Pattern of triangles is radial. However with revolve, there are always two surfaces created.
- The V Grid value for both surfaces should be the same. That means the number of legs of the stars can never be an odd number. Fail.

Attempt 5: Incompleted revolve with curved surface

A full 360 degree revolve will always produce 2 surfaces which can not make a star with odd number of legs. However an incompleted revolve will make a single surface.

- Create a ring form as in Attempt 4.
- Select the form, in the properties box, under Constraints, associate “Start Angle” with a parameter “Start Sweep”. Associate “End Angle” with a parameter “End Sweep”.
- Create a parameter (integer) ” No of Legs” under Other.
- Create prameters (integers) “N1” and “N2”.
- In Family Editor, set a formula for N1 = 2 * No of Legs. Set a formula for N2 = N1 – 1.
- Set a formula for Start Sweep = 360°/(2 * N1). Set a formula for End Sweep = 360° – Start Sweep.
- Select the ring surface, divide surface with triangle (bent), set U Grid layout as None, associate V Grid Number with parameter “N2”.
- Now I have a radial triangular pattern which ends with half a triangle.
- By changing the value of parameter “No of Legs”, the number of triangles changes. Note the pattern always ends with half a triangle.
- The plan: place a star leg (5 points adaptive component) at every triangle. Complete the star by placing another star leg at the end of the ring surface.

**Placing the Leg**

- Place a point at the center.
- Select the XY plane of the center point, place another point on it. Move the new point up by giving it an offset value. Associate the offset value with a parameter “H”.
- Load the 5 points adaptive component leg from Method 2C. Place a leg at one of the triangle by a adapting to the 3 points of the triangle, the center point and the point above the center.
- Select the leg, repeat.

**Placing the Last Leg**

- Place a point on the inner circle close to the last leg.
- Select the point, in the properties box, under Dimensions, associate “Normalized Curve Parameter” to a parameter “X”.
- In Family Editor, set formula of X = (N2 – 1)/N2.
- Select the divided surface and turn off “Pattern” and “Surface”. This will show the original surface.
- Place a 5 point adaptive leg by adapting to the vertex of original surface, the point on the inner circle, the point at center, the vertex of the starting leg and the point above the center.
- Finally, test by flexing parameters “No of Legs”, R1, R2, and H.