'iperboloide_v3

'i. riparametrizzati i raggi
'ii. cambiata eccentricità
'iii. aggiunto iperboloide interno (resta da verificare r_base)
'iv. aggiunta seconda elica

Rhino.enableRedraw False
Rhino.command "_SelAll"
Rhino.command "_Delete"

	
'dimensional parameter
	
'heigth[m]
h_base=1
h_top=11
'radius [m]
r_bottleneck=2
delta_r_base=1
	
	
'wind direction parameter
	
'rotation: counterclockwise [degrees]
counterclockwise=0	
'eccentricity: r_y/r_x [1,+oo
eccentricity=1
'downwind shift [m]  
shift=0
'downwind lift  [m]
lift=0


'elix parameter

'revolution number
revolutions=5
'elix count
count=1


Call pointassignment()
Rhino.enableRedraw True

Sub pointassignment()
	' _creates a number of Array contaning a n*m grid of points 
	' defining different surfaces, according to corresondent function.
	' _create elix as well
	
	n = 50
	m = 50
	
	rm=revolutions*m
	

	Dim pts_hyp() ' points on outer hyperboloid
	ReDim pts_hyp(n*m-1) ' n x m elemnts, from 0 to n*m-1
	
	
	Dim pts_inthyp() ' points on inner hyperboloid
	ReDim pts_inthyp(n*m-1) 
	
	Dim pts_core() ' points on cylindric core
	ReDim pts_core(n*m-1) 
	
	Dim pts_extelix() '  points on outer elix
	ReDim pts_extelix(3*rm-1) ' 3 points per row, revolutions*m rows 

	Dim pts_intelix() '  points on inner elix
	ReDim pts_intelix(3*rm-1) 
	
	
	' rows
	For i=0 To n-1
		u = i/(n-1) ' u va da 0 a 1
		' columns
		For j = 0 To m-1
			v = j/(m-1) ' v va da 0 a 1 
            
			' (i,j)-th point has (i*m+j)-th position
			pts_hyp(i*m+j) = hyperboloid(u,v)
			pts_inthyp(i*m+j) = hyperboloid_interior(u,v)
			pts_core(i*m+j) = centralcore_physical(u,v)
			
		Next
	Next
  
	' drawing hyperboloids and core surfaces
	Rhino.addSrfPtGrid Array(n,m), pts_hyp
	Rhino.addSrfPtGrid Array(n,m), pts_inthyp
	Rhino.addSrfPtGrid Array(n,m), pts_core
	
	
	For l=0 To count-1
		
		For k=0 To rm-1
		
			'elix parametric intrinsic coordinate
			v = k/(rm-1) ' u va da 0 a 1
			u=v*revolutions+l/(count)
			
			'elix points
			pts_extelix(3*k + 0)=hyperboloid(u-0.25,v)
			pts_extelix(3*k + 1)=midpoint_ext(u-0.25,v)
			pts_extelix(3*k + 2)=hyperboloid_interior(u-0.25,v)
		
			pts_intelix(3*k + 0)=hyperboloid_interior(0.25-u,v)
			pts_intelix(3*k + 1)=midpoint_int(0.25-u,v)
			pts_intelix(3*k + 2)=centralcore(0.25-u,v)
		
		Next
	
		' drawingelix
		Rhino.addSrfPtGrid Array(rm,3), pts_extelix	
		Rhino.addSrfPtGrid Array(rm,3), pts_intelix	
	
	Next
End Sub

Function hyperboloid(u,v)
	' hyperboloid(u,v) defines outer hyerboloid surface
	' calculatin for each (u,v) couple its correspondent 3d point
	' u&v are curvilinear surface's coordinates. 
	' NOTE: sections on the top have same area.
	
	'conversions
	counterclockwise_r=Rhino.Pi*counterclockwise/180	
	r_base=r_bottleneck+delta_r_base
	
	'cylindrical coordinates
	theta=2*Rhino.Pi*u
	z=(h_top-h_base+0.5*lift*(cos(theta+Rhino.pi)-1))*(-v)
	r=Sqr((r_bottleneck)^2+ _
		(2*delta_r_base*r_bottleneck+delta_r_base^2)*(-v)^2)		
	
	'cartesian coordinates
	x=r*(cos(theta))+shift*(r-r_bottleneck)/r_base
	y=r*eccentricity*sin(theta)
	
	'rotating/traslating
	x_finale=x*cos(counterclockwise_r)-y*sin(counterclockwise_r)
	y_finale=x*sin(counterclockwise_r)+y*cos(counterclockwise_r)
	z_finale=z+h_top
	
	hyperboloid = Array(x_finale,y_finale,z_finale)  
	
End Function

Function hyperboloid_interior (u,v)
	'hyperboloid_interior(u,v) defines inner hyerboloid surface
	'NOTE: section on the base do NOT have same area
	
	'conversions
	counterclockwise_r=Rhino.Pi*counterclockwise/180	
	r_top=Sqr(0.5*(r_bottleneck^2+(3.5/2)^2))
	delta_r_intbase=delta_r_base/2
	r_intbase=r_top+delta_r_intbase	
	
	'cylindrical coordinates
	theta=2*Rhino.Pi*u
	z=(h_top-0.7*h_base)*(-v)
	r=Sqr((r_top)^2+ _
		(2*delta_r_intbase*r_top+delta_r_intbase^2)*(-v)^2)		
	
	'cartesian coordinates
	x=r*(cos(theta))+shift*(r-r_top)/r_intbase
	y=r*eccentricity*sin(theta)
	
	'rotating/traslating
	x_finale=x*cos(counterclockwise_r)-y*sin(counterclockwise_r)
	y_finale=x*sin(counterclockwise_r)+y*cos(counterclockwise_r)
	z_finale=z+h_top
	
	hyperboloid_interior = Array(x_finale,y_finale,z_finale)  
	
End Function

Function centralcore(u,v)
	' centralcore(u,v) defines core surface, whose (u,v) points
	' are in correspondence with hyperboloyd(u,v) points
	

	'cylindrical coordinates
	theta=2*Rhino.Pi*u
	z=v*(h_base-h_top)+h_top
	r=3.5/2 '[m]
		
	'cartesian coordinates
	x=r*cos(theta)
	y=r*sin(theta)
		
	centralcore = Array(x,y,z) 

End Function

Function centralcore_physical(u,v)
	' centralcore_physical(u,v) defines core real surface

	'coordinate cilindriche
	theta=2*Rhino.Pi*u
	z=(h_top+h_base)*v
	r=3.5/2
		
	'coordinate cartesiane
	x=r*cos(theta)
	y=r*sin(theta)
		
	centralcore_physical = Array(x,y,z) 

End Function

Function midpoint_ext(u,v)
	' finds midpoint betwene correspondent (u,v) in outer and inner hyperboloid
	
	hyp=hyperboloid(u,v)
	cc=hyperboloid_interior(u,v)
	midpoint_ext=Array( _
		0.5*(hyp(0)+cc(0)), _
		0.5*(hyp(1)+cc(1)), _
		0.5*(hyp(2)+cc(2)))

End Function

Function midpoint_int(u,v)
	' finds midpoint between correspondent (u,v) in inner hyperboloid and core
		
	hyp=hyperboloid_interior(u,v)
	cc=centralcore(u,v)
	midpoint_int=Array( _
		0.5*(hyp(0)+cc(0)), _
		0.5*(hyp(1)+cc(1)), _
		0.5*(hyp(2)+cc(2)))

End Function