# Copyright Tony Kaap 2008
# regularSphere.py
# This script can be used for any legal purpose as long as this attribution
# remains intact.


#example usages:

#import geodesic
#reload(geodesic)
#geodesic.checkFaceDistribution()



#import maya.cmds as m
#import geodesic
#reload(geodesic)
#for n in range(5): # smoothing iterations
#	for i in range(5): # types
#		print "I: " + str(i)
#		o2 = geodesic.geodesicSolid(n,i)
#		m.move(3*i,0,3*n,o2)



import maya.cmds as m

# n - number of division steps to take
# type - which type of platonic solid to start with. (only types 1 and 2 are
# effective here.)
#
# 0 - Dodecahedron -- poke faces
# 1 - Icosahedron (already works)
# 2 - Octahedon ( already works)
# 3 - Tetrahedron (move +y 0.354*radius)  UnitSphere scaled up to 1.061 circumscribes this.
# 4 - Cube 

def geodesicSolid(n,type=1,obj=None):
	if (type < 0 or type > 4):
		print "Error: Select a type value between 0 and 4:"
		return
		
	if(type < 4):
		obj = m.polyPlatonicSolid( r=1, st=type)[0]
		#tetrahedron -- needs extra work to get it centered properly
		if type == 3: 
			# since Maya does not start the tetrahedron with its true center at the
			# origin, and since the calculated bounding box for it is based off of
			# the axes, and not well suited for its singular shape, I move the 
			# object to the world origin, then combine it with a large sphere
			# with the same center, will forces the sculpt deformer to accurately
			# deform the tetrahedral points into a true geodesic shape.
			m.move(0, 0.354,0, obj, r=1)
			tObj = m.polyCube(w=n*2, d=n*2, h=n*2)[0]
			obj = m.polyUnite(obj,tObj)[0]
	else: #cube!
		obj = m.polyCube(w=1,d=1,h=1)[0]
	if(type ==0 or type ==4):
		m.polyPoke(obj, ws=1, tx=0, ty=0, tz=0, ch=1)
 		
	
	print "using " +obj
	m.select(obj)
	
	# preparation steps to make the various solids easier to "geodesize"
	
	for i in range(n):
		print i
		# This is an alternate method to smoothing.  I'm not sure which is better,
		# since the results are very close.  I'll keep it here in case it 
		# becomes clearly better later.
			#numEdges = m.polyEvaluate(obj,e=1)
			#m.select(obj+".e[0:"+str(numEdges-1)+"]")
			#m.polySubdivideEdge(obj+".e[0:"+str(numEdges-1)+"]", ws=0, s=0, dv=1)
			#numEdges *=2
			#m.polyTriangulate (obj+".e[0:"+str(numEdges-1)+"]");
			#m.select(obj)
		m.polySmooth(obj,mth=1,dv=1,c=1, suv=1,peh=0,sl=1,dpe=1, ps=0.1, ro=1,ch=1)
		m.sculpt(obj,mode="stretch", insideMode="even", maxDisplacement=0, dropoffType="linear", dropoffDistance=1, groupWithLocator=0, objectCentered=1)
		m.delete(obj,ch=1)
		# shink the non-final steps, so that the subsequent sculpt deformer
		# will stretch the shape properly
		if i != n-1:
			m.scale(0.75, 0.75, 0.75,obj)
			m.makeIdentity(obj, apply=1, t=1,r=1,s=1,n=0)
	
	if (type == 3): # clean-up tetrahedron
		objList = m.polySeparate(obj)
		#print objList
		m.delete(objList[1:2])
		obj = objList[0]
	m.delete(obj,ch=1)
	return obj
		
		
# this is a more general case if you want to perform the geodesic operation
# on some non-standard geometry.
#		
def geodesize(n=1,obj=None):
	if not obj:
		obj = m.ls(sl=1)[0]
	for i in xrange(n):
		m.polySmooth(obj,mth=1,dv=1,c=1, suv=1,peh=0,sl=1,dpe=1, ps=0.1, ro=1,ch=1)
		m.sculpt(obj,mode="stretch", insideMode="even", maxDisplacement=0, dropoffType="linear", dropoffDistance=1, groupWithLocator=0, objectCentered=1)
		m.delete(obj,ch=1)
		if i != n-1:
			m.scale(0.75, 0.75, 0.75,obj)
			m.makeIdentity(obj, apply=1, t=1,r=1,s=1,n=0)
	m.select(obj)
	return obj
		
		
# This is a script to check how regular of an object is created.  It starts with
# the surface area of each face, then finds the average, min, and max face size.  
# The closer the avg, min, and max are together, the more regular the surface is.
	
# Because the polyEvaluate -area command only works on separate mesh objects,
# you need to run 'extract' with 'keep faces together turned off', then select the resulting individual objects. before running this.
def checkFaceDistribution():
	list = m.ls(sl=1)
	print "number of objects selected: " + str(len(list))
	if len(list) == 0:
		print "checkFaceDistribution: select some face-objects to check!"
		return
	sum = 0
	min = 1000
	minIndex = -1
	max = 0;
	maxIndex = -1
	index = 0
	for face in list:
		area = m.polyEvaluate(face, area=1)
		sum += area
		if area > max:
			max = area
			maxIndex = index
		if area < min:
			min = area
			minIndex = index
		index += 1
	
	avg = sum / len(list)
	maxPercent = max / avg
	minPercent = min / avg
	print "total= %(sumNum)1.5f" % {'sumNum':sum}
	print 'max = %(maxNum)1.5f - %(maxIndexNum)d - %(maxPercentNum)1.2f%%' %{'maxNum':max, 'maxIndexNum':maxIndex, 'maxPercentNum':maxPercent}
	print 'min = %(minNum)1.5f - %(minIndexNum)d - %(minPercentNum)1.2f%%' %{'minNum':min, 'minIndexNum':minIndex, 'minPercentNum':minPercent}
	print "average = %(avgNum)1.5f"% {'avgNum':avg}

# 
# 0:
# number of objects selected: 20
# total= 9.57454
# max = 0.47873 - 3 - 1.00%
# min = 0.47873 - 8 - 1.00%
# average = 0.47873
# 
# 1:
# number of objects selected: 80
# total= 14.11578
# max = 0.20013 - 18 - 1.13%
# min = 0.16855 - 55 - 0.96%
# average = 0.17645
# 
# 2:
# number of objects selected: 320
# total= 14.91912
# max = 0.05531 - 250 - 1.19%
# min = 0.04360 - 318 - 0.94%
# average = 0.04662
# 
# 3:
# number of objects selected: 1280
# total= 15.13286
# max = 0.01420 - 42 - 1.20%
# min = 0.01099 - 1034 - 0.93%
# average = 0.01182	
# 
# 4:
# number of objects selected: 5120
# total= 15.18714
# max = 0.00358 - 426 - 1.21%
# min = 0.00275 - 298 - 0.93%
# average = 0.00297
# 
# 5:
# number of objects selected: 20480
# total= 15.20076
# max = 0.00090 - 10922 - 1.21%
# min = 0.00069 - 16554 - 0.93%
# average = 0.00074
# 
#