def get_bezier_curve_edgematrix(p1, i1, i2, p2, step=30):
"""
Generates an EdgeMatrix of lines representing a bezier curve.
Parameters:
p1: list, the first endpoint of the bezier curve
i1: list, the first influence point of the bezier curve
i2: list, the second influence point of the bezier curve
p2: list, the second endpoint of the bezier curve
step: int (optional), the number of steps to use when drawing splines
for the hermite curve
"""
def x(t):
return Generator.get_bezier_function(p1[0], i1[0], i2[0], p2[0])(t)
def y(t):
return Generator.get_bezier_function(p1[1], i1[1], i2[1], p2[1])(t)
def z(t):
return 0
parametric = Parametric(x, y, z)
edgematrix = EdgeMatrix()
step_range = Generator.get_step_range(0, 1, step)
for i in range(len(step_range) - 1):
edgematrix.add_edge(parametric.get_point(step_range[i]),
parametric.get_point(step_range[i + 1]))
return edgematrix
def get_polygon_edgematrix(center_x, center_y, radius, sides):
"""
Generates an EdgeMatrix of lines representing a regular polygon
centered at the given points inscribed within a circle of the
given radius.
Parameters:
center_x: int, the x coordinate of the center of the polygon
center_y: int, the y coordinate of the center of the polygon
radius: int, the radius of the circle
sides: int, the number of sides in the polygon
"""
def x(t):
return cos(t) * radius + center_x
def y(t):
return sin(t) * radius + center_y
def z(t):
return 0
parametric = Parametric(x, y, z)
edgematrix = EdgeMatrix()
step_range = Generator.get_step_range(0, 2 * pi, sides)
for i in range(len(step_range) - 1):
edgematrix.add_edge(parametric.get_point(step_range[i]),
parametric.get_point(step_range[i + 1]))
return edgematrix
def get_hermite_curve_edgematrix(p1, r1, p2, r2, step=30):
"""
Generates an EdgeMatrix of lines representing a hermite curve.
Parameters:
p1: list, the first point of the hermite curve
r1: list, the rate of change at p1
p2: list, the second point of the hermite curve
r2: list, the rate of change at p2
step: int (optional), the number of steps to use when drawing splines
for the hermite curve
"""
points = Matrix(matrix=[p1, p2, r1, r2])
inverse = Matrix([[2, -2, 1, 1], [-3, 3, -2, -1], [0, 0, 1, 0],
[1, 0, 0, 0]])
c = inverse * points
def x(t):
return Generator.get_hermite_function(c[0][0], c[1][0], c[2][0],
c[3][0])(t)
def y(t):
return Generator.get_hermite_function(c[0][1], c[1][1], c[2][1],
c[3][1])(t)
def z(t):
return 0
parametric = Parametric(x, y, z)
edgematrix = EdgeMatrix()
step_range = Generator.get_step_range(0, 1, step)
for i in range(len(step_range) - 1):
edgematrix.add_edge(parametric.get_point(step_range[i]),
parametric.get_point(step_range[i + 1]))
return edgematrix
def get_hermite_curve_edgematrix(p1, r1, p2, r2, step=30):
"""
Generates an EdgeMatrix of lines representing a hermite curve.
Parameters:
p1: list, the first point of the hermite curve
r1: list, the rate of change at p1
p2: list, the second point of the hermite curve
r2: list, the rate of change at p2
step: int (optional), the number of steps to use when drawing splines
for the hermite curve
"""
points = Matrix(matrix=[p1, p2, r1, r2])
inverse = Matrix([
[2, -2, 1, 1],
[-3, 3, -2, -1],
[0, 0, 1, 0],
[1, 0, 0, 0]])
c = inverse * points
def x(t): return Generator.get_hermite_function(
c[0][0], c[1][0], c[2][0], c[3][0])(t)
def y(t): return Generator.get_hermite_function(
c[0][1], c[1][1], c[2][1], c[3][1])(t)
def z(t): return 0
parametric = Parametric(x, y, z)
edgematrix = EdgeMatrix()
step_range = Generator.get_step_range(0, 1, step)
for i in range(len(step_range) - 1):
edgematrix.add_edge(parametric.get_point(step_range[i]),
parametric.get_point(step_range[i + 1]))
return edgematrix
def get_polygon_edgematrix(center_x, center_y, radius, sides):
"""
Generates an EdgeMatrix of lines representing a regular polygon
centered at the given points inscribed within a circle of the
given radius.
Parameters:
center_x: int, the x coordinate of the center of the polygon
center_y: int, the y coordinate of the center of the polygon
radius: int, the radius of the circle
sides: int, the number of sides in the polygon
"""
def x(t): return cos(t) * radius + center_x
def y(t): return sin(t) * radius + center_y
def z(t): return 0
parametric = Parametric(x, y, z)
edgematrix = EdgeMatrix()
step_range = Generator.get_step_range(0, 2 * pi, sides)
for i in range(len(step_range) - 1):
edgematrix.add_edge(parametric.get_point(step_range[i]),
parametric.get_point(step_range[i + 1]))
return edgematrix
def get_bezier_curve_edgematrix(p1, i1, i2, p2, step=30):
"""
Generates an EdgeMatrix of lines representing a bezier curve.
Parameters:
p1: list, the first endpoint of the bezier curve
i1: list, the first influence point of the bezier curve
i2: list, the second influence point of the bezier curve
p2: list, the second endpoint of the bezier curve
step: int (optional), the number of steps to use when drawing splines
for the hermite curve
"""
def x(t): return Generator.get_bezier_function(
p1[0], i1[0], i2[0], p2[0])(t)
def y(t): return Generator.get_bezier_function(
p1[1], i1[1], i2[1], p2[1])(t)
def z(t): return 0
parametric = Parametric(x, y, z)
edgematrix = EdgeMatrix()
step_range = Generator.get_step_range(0, 1, step)
for i in range(len(step_range) - 1):
edgematrix.add_edge(parametric.get_point(step_range[i]),
parametric.get_point(step_range[i + 1]))
return edgematrix
def draw_line(self, x1, y1, z1, x2, y2, z2, color=Color.BLACK()):
"""
Draws the a line onto the internal raster after applying the current
TransformationMatrix on the stack.
Parameters:
x1: int, the x coordinate of the first endpoint of the line
y1: int, the y coordinate of the first endpoint of the line
z1: int, the z coordinate of the first endpoint of the line
x1: int, the x coordinate of the second endpoint of the line
y1: int, the y coordinate of the second endpoint of the line
z1: int, the z coordinate of the second endpoint of the line
color: Color (optional), the color of the line
"""
self.draw_edgematrix(EdgeMatrix([[x1, y1, z1, 1], [x2, y2, z2, 1]]),
color)
