Add b spline object

Author: RamAddict

data/main.ui

@@ -315,7 +315,7 @@
     <item row="2" column="1" rowspan="2">
      <widget class="QStackedWidget" name="componentWidget">
       <property name="currentIndex">
-       <number>0</number>
+       <number>1</number>
       </property>
       <widget class="QWidget" name="emptyPage">
        <layout class="QVBoxLayout" name="verticalLayout_2">
@@ -379,8 +379,8 @@
             <rect>
              <x>0</x>
              <y>0</y>
-             <width>389</width>
-             <height>322</height>
+             <width>375</width>
+             <height>337</height>
             </rect>
            </property>
            <layout class="QVBoxLayout" name="verticalLayout">
@@ -474,6 +474,11 @@
                   <string>Point</string>
                  </property>
                 </item>
+                <item>
+                 <property name="text">
+                  <string>BSpline</string>
+                 </property>
+                </item>
                 <item>
                  <property name="text">
                   <string>Line</string>

pycg/app.py

@@ -14,7 +14,7 @@
 from PySide2.QtCore import Qt, QPoint
 
 from blas import Vector, Matrix
-from graphics import (Painter, Camera, Transformation, Drawable, Point, Line,
+from graphics import (BSpline, Painter, Camera, Transformation, Drawable, Point, Line,
                       Wireframe, Polygon, Color, Bezier)
 from utilities import experp, begin, sign, to_float
 import obj as wavefront_obj
@@ -189,6 +189,8 @@ def new_object():
                 obj = Polygon([Point(x, y) for x, y in parsed])
             elif typename == "Bezier" and len(parsed) > 2:
                 obj = Bezier([Point(x, y) for x, y in parsed])
+            elif typename == "BSpline" and len(parsed) > 2:
+                obj = BSpline([Point(x, y) for x, y in parsed])
             else:
                 return
 

pycg/graphics.py

@@ -234,6 +234,9 @@ class Bezier(Wireframe):
     def __init__(self, points: Sequence[Point], step=0.01):
         super().__init__(bezier(points, step))
 
+class BSpline(Wireframe):
+    def __init__(self, points: Sequence[Point], step=0.01):
+        super().__init__(bSpline(points, step))
 
 class Polygon(Wireframe):
     """Filled polygon."""
@@ -587,3 +590,35 @@ def bezier(points: Sequence[Point], step: float) -> Sequence[Point]:
     else:
         return points
     return curve
+
+def bSpline(points: Sequence[Point], step: float) -> Sequence[Point]:
+    curve = []
+    if len(points) == 3:
+        points = [points[0], points[1], points[1], points[2]]
+    if len(points) >= 4:
+        d1 = step
+        d2 = step*step
+        d3 = step*step*step
+        E = Matrix([0,    0,    0, 1], 
+                   [d3,   d2,  d1, 0], 
+                   [6*d3, 2*d2, 0, 0], 
+                   [6*d3, 0,    0, 0])
+        M = (1/6)*Matrix([-1, 3,-3, 1], 
+                         [ 3,-6, 3 ,0], 
+                         [-3, 0, 3, 0], 
+                         [ 1, 4, 1, 0])
+        ExM = E @ M
+        for i in range(0, len(points)-3):
+            G = Vector(points[i], points[i+1], points[i+2], points[i+3])
+            D = ExM @ G
+            j = 0
+            while True:
+                j += step
+                if j >= 1: break
+                curve.append(Point(D[0][0], D[0][1]))
+                D[0] += D[1]
+                D[1] += D[2]
+                D[2] += D[3]
+    else:
+        return points
+    return curve