def draw_circle_x_y(draw,
r,
center=np.array([1, 1]),
radius=1,
start=np.array([0.0, 1.0, 0.0]),
arcExtent=180.0,
rgba=(102, 255, 51),
width=5,
shift=np.array([1000, 1000, 0]),
scale=200):
"""
Draws a circle in the x-y plane.
args:
center : The center of the circle in original coordinate system.
radius : The radius of the circle in original coordinate system.
"""
start = start * radius
if len(center) == 2:
center = np.concatenate((center, np.array([0])), axis=0)
center = np.dot(r, center) * scale
shift1 = shift[:3] + center
pt1 = np.dot(r, start)
##
theta = np.pi * 1.0 / 180.0
rot = general_rotation(np.dot(r, np.array([0, 0, 1])), theta)
for j in range(0, int(arcExtent)):
pt2 = np.dot(rot, pt1)
draw.line((pt1[0] * scale + shift1[0], pt1[1] * scale + shift1[1],
pt2[0] * scale + shift1[0], pt2[1] * scale + shift1[1]),
fill=rgba,
width=width)
pt1 = pt2
def generalized_arc(draw,
r,
center,
vec,
point,
radius,
prcnt=1,
rgba=(255, 0, 0, 100),
scale=200,
shift=np.array([1000, 1000, 0]),
width=5):
"""
Same as generalized_circle, but instead of drawing the whole circle, only draws a portion of it.
"""
pt1 = np.dot(r, point)
vec = vec / sum(vec**2)**0.5
theta = np.pi * 2.0 / 80.0 * prcnt
r1 = general_rotation(np.dot(r, vec), theta)
for j in range(0, 80):
pt2 = np.dot(r1, pt1)
#draw.ellipse( (pt2[0]-2,pt2[1]-2,pt2[0]+2,pt2[1]+2), fill = (68,193,195), outline = (68,193,195))
draw.line((pt1[0] * scale + shift[0], pt1[1] * scale + shift[1],
pt2[0] * scale + shift[0], pt2[1] * scale + shift[1]),
fill=rgba,
width=width)
pt1 = pt2
def generalized_circle(draw,
center,
vec,
radius,
rotation_matrix,
scale=100,
shift=np.array([1000, 1000, 0]),
rgba=(255, 122, 0, 100),
width=5):
"""
Draws a circle as seen from a given angle.
args:
draw: The draw object associated with image we are plotting on. Used to make lines, ellipses and planes on it.
center: The center of the circle. Provided in original coordinates (see file header). Example: [0,0,0]
vec: The vector that passes through the center and is perpendicular to the plane of the circle.
Provided in original coordinates (see file header). Example: np.array([0,0,1])
radius: the radius of the circle.
scale: The amount by which the whole plot is to be scaled.
shift: The origin corresponds to this pixel on the images (first two coordinates).
rgba: The color of the line.
"""
# Make the vec a unit vector by dividing it by its length
vec = vec / sum(vec**2)**0.5
if vec[0] == 0 and vec[1] == 0:
# Let's say the vec is [0, 0, z]. [0, 0, z]*[1, 1, 0] will be always
# [0, 0, 0].
orthogonal_vec = np.array([1, 1, 0])
else:
# For example, the orthogonal vector of [2, 1, 0] is [-1, 2, 0].
orthogonal_vec = np.array([vec[1], -vec[0], 0])
# Normalizing
orthogonal_vec = orthogonal_vec / sum(orthogonal_vec**2)**0.5
# We are drawing the circle from the rotation_starting_point
rotation_starting_point = center + radius * orthogonal_vec
rotation_starting_point = np.dot(rotation_matrix, rotation_starting_point)
# We complete drawing the circle with 80 steps
theta = np.pi * 2.0 / 80.0
# runner is a 3-dimensional rotation matrix that rotates by incremental
# amount.
runner = general_rotation(np.dot(rotation_matrix, vec), theta)
for j in range(0, 80):
rotation_ending_point = np.dot(runner, rotation_starting_point)
draw.line((rotation_starting_point[0] * scale + shift[0],
rotation_starting_point[1] * scale + shift[1],
rotation_ending_point[0] * scale + shift[0],
rotation_ending_point[1] * scale + shift[1]),
fill=rgba,
width=width)
rotation_starting_point = rotation_ending_point
def project_circle_on_plane(draw,
r,
center=np.array([1, 1]),
radius=1,
plane=np.array([4.5, 4.5, 4.5]),
start=np.array([0.0, 1.0, 0.0]),
arcExtent=180.0,
shift=np.array([1000, 1000, 0]),
scale=200):
"""
Draws the projection of a circle onto a plane.
args:
center : The center of the circle in original coordinate system.
radius : The radius of the circle in original coordinate system.
plane : The intercepts of the plane on the x, y and z axes.
start : The point at which to start drawing the arc. It should be ensured that this point lies on the circle.
arcEctent : The angle the arc is to make.
"""
[a, b, c] = plane
center = np.concatenate((center, np.array([0])), axis=0)
center1 = np.dot(r, center) * scale
shift1 = shift[:3] + center1
pt1 = np.dot(r, start)
[x, y] = np.array([0.0, radius])
z = c * (1 - x / a - y / b)
pt1Up = np.dot(r, np.array([x, y, z]))
##
theta = np.pi * 1.0 / 180
rot = general_rotation(np.dot(r, np.array([0, 0, 1])), theta)
for j in range(0, arcExtent):
pt2 = np.dot(rot, pt1)
pt2Orig = np.dot(np.transpose(r), pt2) + center
[x, y] = pt2Orig[:2]
z = c * (1 - x / a - y / b)
pt2Up = np.dot(r, np.array([x, y, z]))
if sum((pt1Up - pt2Up)**2) < 0.1:
draw.line(
(pt1Up[0] * scale + shift[0], pt1Up[1] * scale + shift[1],
pt2Up[0] * scale + shift[0], pt2Up[1] * scale + shift[1]),
fill=(102, 102, 255, 100),
width=5)
#draw.line((pt1Up[0]*scale + shift[0], pt1Up[1]*scale+shift[1], pt2Up[0]*scale+shift[0], pt2Up[1]*scale+shift[1]), fill=(102,255,51,100), width=5)
# The vertical lines clibing up.
draw.line((pt2[0] * scale + shift1[0], pt2[1] * scale + shift1[1],
pt2Up[0] * scale + shift[0], pt2Up[1] * scale + shift[1]),
fill=(51, 102, 255, 60),
width=5)
pt1 = pt2
pt1Up = pt2Up
def project_circle_on_surface(draw,
r,
fn,
center=np.array([0, 0]),
radius=0.75,
start=np.array([0.0, 0.75, 0.0]),
arcExtent=180.0,
shift=np.array([1000, 1000, 0]),
scale=300):
"""
Draws the projection of a circle onto an arbitrary surface defined by the function, fn.
"""
center = np.concatenate((center, np.array([0])), axis=0)
center1 = np.dot(r, center) * scale
shift1 = shift[:3] + center1
pt1 = np.dot(r, start)
[x, y] = np.array([0.0, radius])
z = fn(np.matrix([x, y]))
pt1Up = np.dot(r, np.array([x, y, z]))
theta = np.pi * 2.0 / 180
rot = general_rotation(np.dot(r, np.array([0, 0, 1])), theta)
for j in np.arange(0, arcExtent):
pt2 = np.dot(rot, pt1)
pt2Orig = np.dot(np.transpose(r), pt2) + center
[x, y] = pt2Orig[:2]
z = fn(np.matrix([x, y]))
pt2Up = np.dot(r, np.array([x, y, z]))
if sum((pt1Up - pt2Up)**2) < 0.1:
draw.line(
(pt1Up[0] * scale + shift[0], pt1Up[1] * scale + shift[1],
pt2Up[0] * scale + shift[0], pt2Up[1] * scale + shift[1]),
fill=(102, 102, 255, 100),
width=7)
# The vertical lines clibing up.
draw.line((pt2[0] * scale + shift1[0], pt2[1] * scale + shift1[1],
pt2Up[0] * scale + shift[0], pt2Up[1] * scale + shift[1]),
fill=(51, 102, 255, 100),
width=8)
pt1 = pt2
pt1Up = pt2Up
def generalized_circle2(draw,
center,
vec,
radius,
r,
scale=200,
shift=np.array([1000, 1000, 0]),
rgba=(255, 20, 147, 250),
width=5):
"""
Basically the same as generalized_circle but the center and vec are expected in the rotated coordinates (image coordinates).
args:
draw: The draw object associated with image we are plotting on. Used to make lines, ellipses and planes on it.
center: The center of the circle. Provided in image coordinates (see file header).
vec: The vector that passes through the center and is perpendicular to the plane of the circle. Provided in image coordinates (see file header).
radius: the radius of the circle.
scale: The amount by which the whole plot is to be scaled.
shift: The origin corresponds to this pixel on the images (first two coordinates).
rgba: The color of the line.
"""
vec = vec / sum(vec**2)**0.5
if vec[0] == 0 and vec[1] == 0:
orthogonal_vec = np.array([1, 1, 0])
else:
orthogonal_vec = np.array([vec[0], -vec[1], 0])
orthogonal_vec = orthogonal_vec / sum(orthogonal_vec**2)**0.5
pt1 = np.dot(r, center) + radius * np.dot(r, orthogonal_vec)
# Make the parameter 30000 smaller for grainy drawing
theta = np.pi * 2.0 / 30.0
r1 = general_rotation(np.dot(r, vec), theta)
for j in range(0, 30):
pt2 = np.dot(r1, pt1)
draw.line((pt1[0] * scale + shift[0], pt1[1] * scale + shift[1],
pt2[0] * scale + shift[0], pt2[1] * scale + shift[1]),
fill=rgba,
width=width)
pt1 = pt2