Coon's Patch: Bezier Curve

Question

I have a text file that has four sets of points. In each set, the first and last points are the start and end points of a curve, and the middle two are the coordinates for two handle points. I have to generate Coon's patch. I only know that these four sets of control points define Coon's patch's boundary. Can anyone guide me further? I have to write a Python script for this, and I am not sure where or how to start. Can anyone explain or point to a resource where I can check out what Coon's patch is? I am new to blender

EDIT: I have drawn the bezier curves. I know the formula for coon's patch but i cannot find how to draw that with script in blender

import bpy
import numpy as np
from bpy import context, data, ops

def new_bezier_point (p0, p0hr, p1hl, p1, t):
    t1 = p0 + (p0hr - p0) * t
    t2 = p0hr + (p1hl - p0hr) * t
    t3 = p1hr + (p1 - p1hl) * t
    p2hl = t1 + (t2 - t1) * t
    p2hr = t2 + (t3 - t2) * t
    p2 = p2hl + (p2hr - p2hl) * t
    return [t1, p2hl, p2, p2hr, t3]






file1 = open('C:\\Users\\yuno gasai\\Downloads\\A3-2 (1)\\A3-2\\coons_patch_points.txt', 'r')
Lines = file1.readlines()
Lines=np.array(Lines)
Lines=Lines.reshape((4,4))



       
for i in Lines:
        c=i[0].split()
        l=i[1].split()
        r=i[2].split()
        e=i[3].split()                                      
        
        coords = [np.array([float(c[0]),float(c[1]),float(c[2])]), np.array([float(l[0]),float(l[1]),float(l[2])]), np.array([float(r[0]),float(r[1]),float(r[2])]), np.array([float(e[0]),float(e[1]),float(e[2])])]
        
        curveData = bpy.data.curves.new('myCurve', type='CURVE')
        curveData.dimensions = '3D'
        curveData.resolution_u = 20
                    
        polyline = curveData.splines.new('BEZIER')

        
        
        
        
        
        
        
        polyline.bezier_points.add(1)
        polyline.bezier_points[0].co = coords[0]
        polyline.bezier_points[0].handle_right=coords[1]
        polyline.bezier_points[1].co = coords[2]
        polyline.bezier_points[1].handle_left=coords[3]
        
        
        curveOB = bpy.data.objects.new('myCurve', curveData)











        scn = bpy.context.scene
        scn.collection.objects.link(curveOB)
        bpy.context.view_layer.objects.active = curveOB
        curveOB.select_set(True)

                        













        obj_data = curveOB.data

        obj_data.fill_mode = 'FULL'

        obj_data.extrude = 0.125

        obj_data.bevel_depth = 0.125

        obj_data.resolution_u = 20
        obj_data.render_resolution_u = 20

And this is what i am trying to implement

Answer 1

EDIT: I posted this back when you were asking only about the curve editing script. I'll check your edit and see if I can update the answer.

import bpy
from mathutils import Vector

C = bpy.context
D = bpy.data

path = D.curves.new("path1", 'CURVE') # create empty curve data
spline = path.splines.new('BEZIER') # create a new spline
spline.bezier_points.add(1) # already has 1 point by default
spline.bezier_points[0].co = spline.bezier_points[0].handle_left = Vector((-1,0,0))
spline.bezier_points[1].co = spline.bezier_points[1].handle_right = Vector((1,0,0))

spline.bezier_points[0].handle_right = Vector((-0.5,0.5,0))
spline.bezier_points[1].handle_left = Vector((0.5,0,0))

curve = D.objects.new("Curve1", path) #make a new object from the data
C.collection.objects.link(curve) # link the object to the scene

This re-creates the default bezier curve. Note that the handles that are outside the bounds (1. left handle and 2. right handle) share the coordinates of their control points. It's not terribly important where they are, but it looks much nicer in edit mode. Of course you can also use this to edit existing curves.