add TP1

README.md

@@ -1,2 +1,25 @@
-# GeoNum2017
-TP Géométrie numérique, spring 2017 
+# GeoNum2017 : Géométrie numérique, spring 2017 
+
+## TP1 : Bézier curves, De Casteljau’s algorithm
+
+### Python
+If you have no prior experience with Python whatsoever, I suggest the tutorial
+[Learn Python in 10 minutes](https://www.stavros.io/tutorials/python/) by Stavros Korokithakis.
+For longer and more complete references, see the [Fast Lane to Python](http://heather.cs.ucdavis.edu/~matloff/Python/PLN/FastLanePython.pdf) by Norm Matloff and, of course, the [official Python 2.7.13 docs](https://docs.python.org/2/).
+
+### NumPy
+[NumPy](http://www.numpy.org/) is a Python package supporting N-dimensional arrays and linear algebra operations. We'll mostly use it to manipulate datapoints stored in matrices (two-dimensional arrays).
+Here is a useful [numpy cheatsheet](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Numpy_Python_Cheat_Sheet.pdf).
+
+### Matplotlib
+[Matplotlib](http://matplotlib.org/) is a Python 2D plotting library -- we'll use it to visualise 2D curves 
+via the [plot](http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.plot) command.
+{% highlight python %}
+# import the modules
+import numpy as np
+import matplotlib.pyplot as plt
+# generate random data
+points = np.random.rand(1000,2)
+# plot
+plt.plot(points[:,0],points[:,1],'bo')
+{% endhighlight %}

TP1/data/infinity.bcv

@@ -0,0 +1,10 @@
+8
+ 0.0      0.0
+-0.7071   0.7071
+-0.9899   0.0
+-0.7071  -0.7071
+ 0.0      0.0
+ 0.7071   0.7071
+ 0.9899   0.0
+ 0.7071  -0.7071
+ 0.0      0.0

TP1/data/simple.bcv

@@ -0,0 +1,5 @@
+3
+ 0 0
+ 3 3
+ 6 4
+ 9 1

TP1/data/spiral.bcv

@@ -0,0 +1,12 @@
+10
+ 10.7112    1.2776 
+ 14.1392    3.3787 
+ 14.3168    6.2451 
+ 12.4736    8.8911 
+  6.0872    8.7484 
+  1.73808   5.2983 
+  6.8796    1.3294 
+ 11.164     4.2866 
+  9.8868    6.1284 
+  8.2216    5.7134 
+  8.06      5.1946 

TP1/tp1.py

@@ -0,0 +1,160 @@
+#------------------------------------------------------
+#
+#  TP1 : Bezier curves, De Casteljau's algorithm
+#  http://tiborstanko.sk/teaching/geo-num-2017/tp1.html
+#  [03-Feb-2017]
+#
+#------------------------------------------------------
+#
+#  This file is a part of the course:
+#    Geometrie numerique (spring 2017)
+#    https://github.com/GeoNumTP/GeoNum2017
+#    M1 Informatique
+#    UFR IM2AG
+#
+#  Course lecturer:
+#    Georges-Pierre.Bonneau at inria.fr
+#
+#  Practical part:
+#    Tibor.Stanko at inria.fr
+#
+#------------------------------------------------------
+
+import sys, os
+import matplotlib.pyplot as plt
+import numpy as np
+
+TP = os.path.dirname(os.path.realpath(__file__)) + "/"
+DATADIR = filename = TP+"data/"
+
+
+#-------------------------------------------------
+# READPOLYGON()
+# Read Bezier control points from a file.
+#
+def ReadPolygon( filename ) :
+    datafile = open(filename,'r');
+    l = datafile.readline()
+    degree = np.fromstring(l,sep=' ',dtype=int)
+    BezierPts = np.fromfile(datafile,count=2*(degree+1),sep=' ',dtype=float)
+    BezierPts = BezierPts.reshape(-1,2)
+    return BezierPts
+
+
+#-------------------------------------------------
+# DECASTELJAU( ... )
+# Perform the De Casteljau algorithm.
+#
+# Input
+#    BezierPts :  #B x 2 matrix of Bezier control points
+#    n         :  upper index of the computed point (depth of the algorithm)
+#    i         :  lower index of the computed point
+#    t         :  curve parameter in [0.0,1.0]
+#
+# Output
+#    point b_i^n from the De Casteljau algorithm.
+#
+def DeCasteljau( BezierPts, n, i, t ) :
+    pass
+    #
+    # TODO : Implement the De Casteljau algorithm.
+    #
+
+
+#-------------------------------------------------
+# BEZIERCURVE( ... )
+# Compute points on the Bezier curve.
+#
+# Input
+#    BezierPts :  #B x 2 matrix of Bezier control points
+#    N         :  number of curve samples
+#
+def BezierCurve( BezierPts, N ) :
+
+    # degree of the curve (one less than the number of control points)
+    degree = BezierPts.shape[0]-1
+
+    # initialize curvepoints as zeros
+    CurvePts = np.zeros([N,2])
+
+    #
+    # TODO : Compute N curve points for t varying uniformly in [0.0,1.0]
+
+    #
+    # hint1:
+    # to generate the uniform sampling of the interval [0.0,1.0] with N elements, use:
+    # >> samples = np.linspace(0.0,1.0,num=N)
+    #
+
+    #
+    # hint2:
+    # to access and change i-th row of the matrix CurvePts, use:
+    # >> CurvePts[i,:]
+    #
+
+    #
+    # hint3:
+    # the actual point b_0^degree on the curve is computed by calling DeCasteljau
+    # with arguments n=degree, i=0.
+    #
+
+    return CurvePts
+
+
+#-------------------------------------------------
+if __name__ == "__main__":
+
+    # arg 1 : data name 
+    if len(sys.argv) > 1 :
+        dataname = sys.argv[1]
+    else :
+        dataname = "simple" # simple, infinity, spiral
+
+    # arg 2 : sampling density
+    if len(sys.argv) > 2 :
+        density = int(sys.argv[2])
+    else :
+        density = 10
+
+    # filename
+    filename = DATADIR + dataname + ".bcv"
+
+    # check if valid datafile
+    if not os.path.isfile(filename) :
+        print "error:  invalid dataname '" + dataname + "'"
+        print "usage:  python tp1.py  [simple,infinity,spiral]  [sampling_density]"
+
+    else :    
+        # read control points
+        BezierPts = ReadPolygon(filename)
+
+        # compute points
+        CurvePts = BezierCurve(BezierPts,density)
+
+        # plot
+        fig = plt.gcf()
+        fig.canvas.set_window_title('TP1 Bezier curves')
+        plt.title(dataname+', '+str(density)+" pts")
+
+        # set axes with equal proportions
+        plt.axis('equal')
+
+        # plot the control polygon
+        plt.plot( BezierPts[:,0], BezierPts[:,1], 'bo-' )
+
+        # plot the curve
+        plt.plot( CurvePts[:,0], CurvePts[:,1], 'r-' )
+
+        #
+        # TODO : Uncomment this if you want to save the render as png image.
+        #
+        #plt.savefig( DATADIR + dataname + ".png" )
+
+        #
+        # TODO : Compute intermediate polygons b_i^k for k=1,...,degree-1 and i=0,...,degree-k
+        #
+        #
+        # TODO : Add plt.plot commands to plot the intermediate polygons
+        #
+
+        plt.show()