def exer2_1():
"""
Plot a rational Bezier curve converting the control vertexes
in polinomial and using the same algorithms of the polinomial.
Test with two different weight sets.
"""
V = np.array([[0,0],[1,2],[3,1]])
W1 = np.array([1,1,1])
W2 = np.array([1,2,1])
fn.drawVertexes(V)
fn.drawVertexes(V,'o')
P1 = fn.bezierRational(V,W1)[0]
P2 = fn.bezierRational(V,W2)[0]
fn.drawVertexes(P1)
fn.drawVertexes(P2)
def exer2_3():
"""
Represents the first quadrant of a circumference using
the rational Bezier curves with control vertexes:
(1,0), (1,1), (0,1)
and weights:
1, sqrt(2)/2, 1.
"""
V = np.array([[1,0],[1,1],[0,1]])
W = np.array([1,math.sqrt(2)/2,1])
fn.drawVertexes(V)
fn.drawVertexes(V,'o')
fn.drawVertexes(fn.bezierRational(V,W)[0])
def exer2_4():
"""
Given the control vertexes:
(1,0), (a,a), (0,1)
for different values of a find the weigths that
represents an arc of circumference.
"""
for a in [0.7, 1., 2., 3.]:
V = np.array([[1,0],[a,a],[0,1]])
W = np.array([1,fn.findArcWeigth(a),1])
centre, radius = fn.findCircle(a)
fn.drawVertexes(fn.circum(centre, radius))
fn.drawVertexes(V)
fn.drawVertexes(V,'o')
fn.drawVertexes(fn.bezierRational(V,W)[0])
def exer2_2():
"""
Increase the grade of a rational Bezier curve converting the
control vertexes in polinomial and using the same algorithms
of the polinomial.
"""
V = np.array([[0,0,0],[1,2,0],[3,2,3],[2,6,2]])
W = np.array([1,1,1,1])
V1,W1 = fn.increaseGradeRational(V, W)
V2,W2 = fn.increaseGradeRational(V1, W1)
V3,W3 = fn.increaseGradeRational(V2, W2)
fn.drawVertexes(fn.bezierRational(V,W)[0])
fn.drawVertexes(V)
fn.drawVertexes(V,'o')
fn.drawVertexes(V1)
fn.drawVertexes(V1,'o')
fn.drawVertexes(V2)
fn.drawVertexes(V2,'o')
fn.drawVertexes(V3)
fn.drawVertexes(V3,'o')
