Creating circles with same edge length.

Coding Python Support
#1

I’m trying to create a bunch of circles with different numbers of vertices in each circle, but with the same edge length. The only way I can think to do this is through the definition of the diameter, but I can’t get anything to work. Can anyone help me? (My attempt is around line 26) Here is my script so far:

 
#Test
import Blender as b
import math
#Just initializing the variables
maxverts = 0
#This is th the length I'd like for all of my edges.
sidelength = 1
scn = b.Scene.GetCurrent()
#Until the user gives an acceptable number of max verts (in the range that Blender allows),
while (maxverts > 100) or (maxverts < 3):
 #keep asking for the maximum number of vertices.
 maxverts = input("What's the max number of verts you want?" )
#Create an empty mesh.
mesh = b.Mesh.New()
obj = scn.objects.new(mesh)
 
#Now make the meshes
#The first numer of vertices is three.
vertnumber = 3
#At this point, I make a list of all of the objects in the scene.
objectlist = []
while vertnumber <= maxverts:
 #This is a formula from geometry, look it up on google if you forgot.
 angle = ((180.0 * (vertnumber - 2))/ vertnumber)
 #This is my best guess at something that I think should work (but doesn't)
 diameter = math.cos(angle / 2) * sidelength
 print math.cos(angle/2)
 print "ANGLE =", angle, "and the vertnumber is", vertnumber, ". OH! Also, the diameter is", diameter
 #make a new circle mesh.
 mesh2 = b.Mesh.Primitives.Circle(vertnumber, diameter) 
 #make it an object, 
 obj2 = scn.objects.new(mesh2)
 #and append it to the list of created objects.
 objectlist.append(obj2)
 #Also, increase the number of vertices created for the next circle.
 vertnumber = vertnumber + 1 
#Merge all of the objects in the object list into one object,
obj.join(objectlist)
#and then delete all of the individual objects.
for object in objectlist:
 scn.objects.unlink(object)
b.Redraw()
print "DOne"

Thanks.

#2

you could use the add primitive circle where all edges are same lenght too

and probably easier to use also ?

hope it helps

#3

Perhaps use the parametric form of the circle eg, and if you are using math angle is radians not degrees


import math

npoints = 5 # number of vertices in circle
r = 1 # radius
for i in range(npoints):
    angle = math.pi*2*i/npoints
    x = r*math.cos(angle)
    y = r*math.sin(angle)
    vertices.append((x,y,0))
#4

@somen:
I’ll try and see if I can get that to work. Thanks for the radians tip.

@RickyBlender:
I don’t understand. What do you mean? I already can make a circle with all its edges the same length, I need to create multiple circles, with different numbers of vertices, that all have the same edge length.

#5

Just in case anyone ever needs to do the same thing in the future (unlikely, but possible), here’s the new version that finally works.

 
#Test
import Blender as b
import math
#Just initializing the variables
maxverts = 0
#This is th the length I'd like for all of my edges.
sidelength = 1
scn = b.Scene.GetCurrent()
#d
while (maxverts > 100) or (maxverts < 3):
 maxverts = input("What's the max number of verts you want?" )
mesh = b.Mesh.New()
obj = scn.objects.new(mesh)
 
#Now make the meshes
vertnumber = 3
objectlist = []
while vertnumber <= maxverts:
 #get the average angle in radians
 angle = ((180.0 * (vertnumber - 2))/ vertnumber) * (math.pi / 180.0)
 
 diameter =  2 * math.sqrt(((sidelength / 2.0) ** 2) + ((math.tan(angle / 2.0) * (sidelength / 2.0)) ** 2))
 print math.cos(angle/2.0), "cos(angle / 2)"
 print "ANGLE =", (angle / 2), "and the vertnumber is", vertnumber, ". OH! Also, the diameter is", diameter
 mesh2 = b.Mesh.Primitives.Circle(vertnumber, diameter)  
 obj2 = scn.objects.new(mesh2)
 objectlist.append(obj2)
 vertnumber = vertnumber + 1 
obj.join(objectlist)
for object in objectlist:
 scn.objects.unlink(object)
b.Redraw()
print "DOne"

Here’s the work that led me to that definition of the diameter. In these equations, i subdivided each exterior edge of a shape, so that the shape would be made up of many right triangles. x is the interior side created by the subdivision.

(edgelength / 2) ^ 2 + (x ^ 2) = (radius ^ 2)
((edgelength / 2) ^ 2) - (radius ^ 2) = - (x ^ 2)

x = tan(angle / 2) * (edgelength / 2)
((edgelength / 2) ^ 2) - (radius ^ 2) = - ((tan(angle / 2) * (edgelength / 2)) ^ 2)
radius ^ 2 = ((tan(angle / 2) * (edgelength / 2)) ^ 2) / ((edgelength / 2) ^ 2)
radius = sqrt(((tan(angle / 2) * (edgelength / 2)) ^ 2) / ((edgelength / 2) ^ 2))
diameter = 2 * radius

#6

if you taking about polygon then you ca add a primitive where you can specify the radius and number of segment

i think this would be easier to calculate then doing circle edge per edge

anyway do you know how tio add a prinitive circle or polygon in python

Thanks

#7

Yeah, I already knew that. But I needed the circles to have the same edge lengths, so I had to do all of that math. If the radius was constant, the edge lengths would change depending on the number of vertices in the circle, which I didn’t want.

#8

there is a simple relationship between the radius and the side lenght for regular polygon

so i tough it would easy to calculate this and the add the primitive circle!

salutations

#9

marky, you are doting the things far more complicated than they really are… Why do you need x (the red line on the drawing below), tan function, square roots, etc…?

http://www.geocities.com/elonsie/Blender/Circle.png

Suppose you number of sides is n and required total length is L, then you simply have:

angle = 2pi()/n
b = L/n
d = 2r = b/sin(angle/2)

Regards,