def draw_object(self, model):
if self.DRAW_LINES:
glLineWidth(1)
glPolygonMode( GL_FRONT_AND_BACK, GL_LINE )
glBegin(GL_TRIANGLES)
for face in model.faces:
for v_id in face.vertex_ids():
vert = model.rendering_verts[v_id]
glColor3f(1,0,0)
glVertex3f(vert[0], vert[1], vert[2])
glEnd()
glPolygonMode(GL_FRONT_AND_BACK, GL_FILL)
glBegin(GL_TRIANGLES)
for face in model.faces:
for v_id in face.vertex_ids():
vert = model.rendering_verts[v_id]
uv = model.uvs[v_id]
glColor3f(1,1,1)
glTexCoord2f(uv[0], uv[1])
glVertex3f(vert[0], vert[1], vert[2])
glEnd()
glBegin(GL_LINES)
glVertex3f(0,-300,0)
vert = model.verts[0]
glVertex3f(vert[0], vert[1], vert[2])
glEnd()
def simulate_triangle(self):
forces = self.wind_forces(self.count)
forces[:, 1] = -1
acc = (self.stepsize * self.stepsize) * linalg.inv(self.mass_matrix).dot(forces)
dist = self.velocities * self.stepsize
s_n = self.rendering_verts + dist + acc
q_n_1 = np.copy(s_n)
b_array = np.zeros((self.n + len(self.fixed_points), 3))
M = self.mass_matrix / (self.stepsize * self.stepsize)
for _ in range(1):
b_array[:self.n] = M.dot(s_n)
for face in self.faces:
f_verts = face.vertex_ids()
for i in range(3):
v1 = f_verts[i]
v2 = f_verts[(i + 1) % 3]
T = self.potential_for_triangle(face, q_n_1, v2)
edge = self.verts[v2] - self.verts[v1]
g = T.dot(edge)
b_array[v1] = b_array[v1] - g
b_array[v2] = b_array[v2] + g
# Assign fixed points
for con_i in range(len(self.fixed_points)):
con = self.fixed_points[con_i]
b_array[-(con_i + 1)] = self.verts[con.vert_a]
q_n_1 = np.linalg.solve(self.global_matrix, b_array)
q_n_1 = q_n_1[:-len(self.fixed_points), :] # Don't grab the unwanted fixed points
self.velocities = ((q_n_1 - self.rendering_verts) * 0.9) / self.stepsize
self.rendering_verts = q_n_1
def calculate_triangle_global_matrix(self):
fixed_point_num = len(self.fixed_points)
M = np.zeros((self.n + fixed_point_num, self.n + fixed_point_num))
M[:self.n, :self.n] = self.mass_matrix
M /= (self.stepsize * self.stepsize)
weights = np.zeros((self.n + fixed_point_num, self.n + fixed_point_num))
weight_sum = np.zeros((self.n + fixed_point_num, self.n + fixed_point_num))
for face in self.faces:
verts = face.vertex_ids()
for k in range(3):
v_1 = verts[k]
v_2 = verts[(k + 1) % 3]
weights[v_1, v_2] += 1
weights[v_2, v_1] += 1
weight_sum[v_1, v_1] += 1
weight_sum[v_2, v_2] += 1
x = weight_sum - weights
for i in range(fixed_point_num):
con = self.fixed_points[i]
x[con.vert_a, -(i + 1)] = 1
x[-(i + 1), con.vert_a] = 1
M[-(i + 1), -(i + 1)] = 0
return x + M
def __init__(self, verts, faces, neighbours=[], uvs = [], constraints=[], flag_type=default_flag_type):
self.flag_type = flag_type
self.n = len(verts)
self.verts = verts
self.rendering_verts = np.copy(verts)
self.faces = faces
self.neighbours = neighbours
for i in range(len(neighbours)):
neighbours[i] = list(set(neighbours[i]))
self.verts_to_tri = []
for i in range(self.n):
in_faces = []
for face in self.faces:
if i in face.vertex_ids():
in_faces.append(face)
self.verts_to_tri.append(in_faces)
self.uvs = uvs
self.stepsize = 0.3
self.velocities = np.zeros((self.n, 3))
self.mass_matrix = np.identity(self.n)
self.constraints = constraints
self.fixed_points = []
for con in self.constraints:
if con.type() == "FIXED":
self.fixed_points.append(con)
if self.flag_type == "imp_tri":
self.mass_matrix /= (len(self.faces))
self.global_matrix = self.calculate_triangle_global_matrix()
self.count = 0
self.wind_magnitude = 5
def simulate_triangle_explicit(self):
forces = self.wind_forces(self.count)
forces[:, 1] = -10
s_n = self.rendering_verts
for face in self.faces:
res_tri_center = face.center_of_triangle(self.verts)
def_tri_center = face.center_of_triangle(s_n)
for vert_id in face.vertex_ids():
T = self.potential_for_triangle(face, s_n, vert_id)
x = self.verts[vert_id] - res_tri_center # bring to origin
x = T.dot(x) # apply rotation
x = x + def_tri_center # reset to original spot
y = (x - s_n[vert_id])
forces[vert_id] = forces[vert_id] + y
acc = (self.stepsize * self.stepsize) * linalg.inv(self.mass_matrix).dot(forces)
dist = self.velocities * self.stepsize
s_n = self.rendering_verts + dist + acc
for con_i in range(len(self.fixed_points)):
con = self.fixed_points[con_i]
s_n[con.vert_a] = self.verts[con.vert_a]
self.rendering_verts = s_n