glm94/terrain_generator
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Changed matrix object names to be more natural. Fixed a bug in the matrix projection math.

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glm94
2020-07-15 09:12:09 -05:00
parent 34f5917359
commit 4ef62ab916
3 changed files with 127 additions and 85 deletions
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engine.py
+4 -4
View File
@@ -38,8 +38,8 @@ class Mesh:
tmp = line.split(' ')
# Subtract one because the obj file isn't zero indexed.
row0 = self.vertices[int(tmp[1]) - 1]
row1 = self.vertices[int(tmp[2]) - 1]
row2 = self.vertices[int(tmp[3]) - 1]
row1 = self.vertices[int(tmp[1]) - 1]
row2 = self.vertices[int(tmp[2]) - 1]
row3 = self.vertices[int(tmp[3]) - 1]
self.triangles.append(Triangle(Matrix3x3(row0, row1, row2)))
self.triangles.append(Triangle(Matrix3x3(row1, row2, row3)))
main.py
+64 -66
View File
@@ -10,7 +10,7 @@ ui = window.Window(600, 600)
near_plane = 0.1
far_plane = 1000.0
fov = 90.0
#'''
tris =[
Matrix3x3(Vector3d(0.0,0.0,0.0),Vector3d(0.0,1.0,0.0),Vector3d(1.0,1.0,0.0)),
Matrix3x3(Vector3d(0.0,0.0,0.0),Vector3d(1.0,1.0,0.0),Vector3d(1.0,0.0,0.0)),
@@ -25,14 +25,16 @@ Matrix3x3(Vector3d(0.0,1.0,0.0),Vector3d(1.0,1.0,1.0),Vector3d(1.0,1.0,0.0)),
Matrix3x3(Vector3d(1.0,0.0,1.0),Vector3d(0.0,0.0,1.0),Vector3d(0.0,0.0,0.0)),
Matrix3x3(Vector3d(1.0,0.0,1.0),Vector3d(0.0,0.0,0.0),Vector3d(1.0,0.0,0.0))
]
#'''
#tris = Mesh()
def main():
#tris.load_obj_file('shuttle.obj')
#tris.load_obj_file('teddy.obj')
ui.thetax = 1
ui.thetay = 1
ui.window.bind('<Left>', left)
ui.window.bind('<Right>', right)
ui.window.bind('<Up>', up)
ui.window.bind('<Down>', down)
ui.window.bind('<ButtonPress-1>', mouse_start)
ui.canvas.bind('<B1-Motion>', mouse_end)
ui.canvas.old_coords = None
@@ -40,27 +42,35 @@ def main():
ui.show()
def left(event):
ui.theta -= .01
ui.thetax -= .1
draw_scene()
def right(event):
ui.theta += .01
ui.thetax += .1
draw_scene()
def up(event):
ui.thetay += .1
draw_scene()
def down(event):
ui.thetay -= .1
draw_scene()
def mouse_start(event):
ui.canvas.old_coords = event.x, event.y
def mouse_end(event):
x, y = ui.canvas.old_coords[0] - event.x, ui.canvas.old_coords[1] - event.y
x, y = event.x - ui.width / 2, event.y - ui.height / 2#ui.canvas.old_coords[0] - event.x, ui.canvas.old_coords[1] - event.y
if x < 0:
ui.theta += .01
ui.thetax -= .01
else:
ui.theta -= .01
print(ui.theta)
ui.thetax += .01
if y < 0:
ui.thetax += .01
ui.thetay -= .01
else:
ui.thetax -= .01
ui.thetay += .01
draw_scene()
#ui.theta += x / ui.width
@@ -69,109 +79,97 @@ def draw_scene():
ui.canvas.delete("all")
#ui.theta += .01 # scaling factor
aspect_ratio = ui.height / ui.width
fov_rad = ui.theta / math.tan(fov * 0.5 / 180.0 * math.pi)
projection_matrix = Matrix4x4.get_projection_matrix(fov, aspect_ratio, near_plane, far_plane)
row0 = Vector4d(aspect_ratio * fov_rad, 0, 0, 0)
row1 = Vector4d(0, fov_rad, 0, 0)
row2 = Vector4d(0, 0, far_plane / (far_plane - near_plane), 1.0)
row3 = Vector4d(0, 0, -far_plane * near_plane / (far_plane - near_plane), 0)
rotation_matrix_y = Matrix4x4.get_y_rotation_matrix(ui.thetax)
projection_matrix = Matrix4x4(row0, row1, row2, row3)
row0 = Vector4d(math.cos(ui.theta), math.sin(ui.theta), 0, 0)
row1 = Vector4d(-math.sin(ui.theta), math.cos(ui.theta), 0, 0)
row2 = Vector4d(0, 0, 1, 0)
row3 = Vector4d(0, 0, 0, 1)
rotation_matrix_z = Matrix4x4(row0, row1, row2, row3)
row0 = Vector4d(1, 0, 0, 0)
row1 = Vector4d(0, math.cos(ui.thetax * 0.5), math.sin(ui.thetax * 0.5), 0)
row2 = Vector4d(0, -math.sin(ui.thetax * 0.5), math.cos(ui.thetax * 0.5), 0)
row3 = Vector4d(0, 0, 0, 1)
rotation_matrix_x = Matrix4x4(row0, row1, row2, row3)
rotation_matrix_x = Matrix4x4.get_x_rotation_matrix(ui.thetay)
triangles = []
for tri in tris:
# Rotate on the z-axis
row0 = rotation_matrix_z.multiply_3d(tri.row0)
row1 = rotation_matrix_z.multiply_3d(tri.row1)
row2 = rotation_matrix_z.multiply_3d(tri.row2)
row1 = rotation_matrix_y.multiply_3d(tri.row1)
row2 = rotation_matrix_y.multiply_3d(tri.row2)
row3 = rotation_matrix_y.multiply_3d(tri.row3)
rotated_z = Matrix3x3(row0, row1, row2)
rotated_y = Matrix3x3(row1, row2, row3)
# Rotate on the x-axis
row0 = rotation_matrix_x.multiply_3d(rotated_z.row0)
row1 = rotation_matrix_x.multiply_3d(rotated_z.row1)
row2 = rotation_matrix_x.multiply_3d(rotated_z.row2)
row1 = rotation_matrix_x.multiply_3d(rotated_y.row1)
row2 = rotation_matrix_x.multiply_3d(rotated_y.row2)
row3 = rotation_matrix_x.multiply_3d(rotated_y.row3)
rotated_x = Matrix3x3(row0, row1, row2)
rotated_x = Matrix3x3(row1, row2, row3)
# The offset into the screen
translated = copy.copy(rotated_x)
translated.row0.z += 3.0
translated.row1.z += 3.0
translated.row2.z += 3.0
translated.row3.z += 3.0
# Use cross-product to get the surface normal (a Vector3d)
x = translated.row1.x - translated.row0.x
y = translated.row1.y - translated.row0.y
z = translated.row1.z - translated.row0.z
x = translated.row2.x - translated.row1.x
y = translated.row2.y - translated.row1.y
z = translated.row2.z - translated.row1.z
line1 = Vector3d(x, y, z)
x = translated.row2.x - translated.row0.x
y = translated.row2.y - translated.row0.y
z = translated.row2.z - translated.row0.z
x = translated.row3.x - translated.row1.x
y = translated.row3.y - translated.row1.y
z = translated.row3.z - translated.row1.z
line2 = Vector3d(x, y, z)
normal = line1.cross_product(line2)
# Now we normalize the normal
w = math.sqrt(normal.x * normal.x + normal.y * normal.y + normal.z * normal.z)
normal.x /= w
normal.y /= w
normal.z /= w
length = math.sqrt(normal.x * normal.x + normal.y * normal.y + normal.z * normal.z)
normal.x /= length
normal.y /= length
normal.z /= length
# Do we display this triangle?
if normal.dot_product(translated.row0) < 0.0:
if normal.dot_product(translated.row1) < 0.0:
# Lighting
light = Vector3d(0, 0, -1) # Shining at the player.
w = math.sqrt(light.x * light.x + light.y * light.y + light.z * light.z)
light.x /= w
light.y /= w
light.z /= w
length = math.sqrt(light.x * light.x + light.y * light.y + light.z * light.z)
light.x /= length
light.y /= length
light.z /= length
dot_product = normal.dot_product(light)
r = abs(int(255 * dot_product))
# Scale into view
row0 = projection_matrix.multiply_3d(translated.row0)
row1 = projection_matrix.multiply_3d(translated.row1)
row2 = projection_matrix.multiply_3d(translated.row2)
row2 = projection_matrix.multiply_3d(translated.row2)
row3 = projection_matrix.multiply_3d(translated.row3)
projected = Matrix3x3(row0, row1, row2)
projected = Matrix3x3(row1, row2, row3)
projected.row0.x += 1
projected.row0.y += 1
projected.row1.x += 1
projected.row1.y += 1
projected.row2.x += 1
projected.row2.y += 1
projected.row0.x *= .5 * ui.width
projected.row0.y *= .5 * ui.height
projected.row3.x += 1
projected.row3.y += 1
projected.row1.x *= .5 * ui.width
projected.row1.y *= .5 * ui.height
projected.row2.x *= .5 * ui.width
projected.row2.x *= .5 * ui.width
projected.row2.y *= .5 * ui.height
projected.row3.x *= .5 * ui.width
projected.row3.y *= .5 * ui.height
t = Triangle(projected)
t.color = r
t.average = (t.coords.row1.z + t.coords.row2.z + t.coords.row3.z) / 3
triangles.append(t)
# Sort the triangles so they are drawn in order.
triangles.sort(key=lambda r: r.average, reverse = True)
for projected in triangles:
r = projected.color
coords = [projected.coords.row0.x, projected.coords.row0.y, projected.coords.row1.x, projected.coords.row1.y, projected.coords.row2.x, projected.coords.row2.y]
coords = [projected.coords.row1.x, projected.coords.row1.y, projected.coords.row2.x, projected.coords.row2.y, projected.coords.row3.x, projected.coords.row3.y]
ui.canvas.create_polygon(coords, fill=from_rgb(r, r, r), outline="black")
ui.canvas.update()
matrix.py
+59 -15
View File
@@ -1,38 +1,82 @@
import vectors
import math
from vectors import Vector3d, Vector4d
class Matrix4x4:
def __init__(self, row0, row1, row2, row3):
if not isinstance(row0, vectors.Vector4d):
raise ValueError("Row must be a Vector4d object.", row0)
if not isinstance(row1, vectors.Vector4d):
def __init__(self, row1, row2, row3, row4):
if not isinstance(row1, Vector4d):
raise ValueError("Row must be a Vector4d object.", row1)
if not isinstance(row2, vectors.Vector4d):
if not isinstance(row2, Vector4d):
raise ValueError("Row must be a Vector4d object.", row2)
if not isinstance(row3, vectors.Vector4d):
if not isinstance(row3, Vector4d):
raise ValueError("Row must be a Vector4d object.", row3)
if not isinstance(row4, Vector4d):
raise ValueError("Row must be a Vector4d object.", row4)
self.row0 = row0
self.row1 = row1
self.row2 = row2
self.row3 = row3
self.row4 = row4
def multiply_3d(self, vector3d):
x = vector3d.x * self.row0.x + vector3d.y * self.row1.x + vector3d.z * self.row2.x + self.row3.x
y = vector3d.x * self.row0.y + vector3d.y * self.row1.y + vector3d.z * self.row2.y + self.row3.y
z = vector3d.x * self.row0.z + vector3d.y * self.row1.z + vector3d.z * self.row2.z + self.row3.z
w = vector3d.x * self.row0.w + vector3d.y * self.row1.w + vector3d.z * self.row2.w + self.row3.w
x = vector3d.x * self.row1.x + vector3d.y * self.row2.x + vector3d.z * self.row3.x + self.row4.x
y = vector3d.x * self.row1.y + vector3d.y * self.row2.y + vector3d.z * self.row3.y + self.row4.y
z = vector3d.x * self.row1.z + vector3d.y * self.row2.z + vector3d.z * self.row3.z + self.row4.z
w = vector3d.x * self.row1.w + vector3d.y * self.row2.w + vector3d.z * self.row3.w + self.row4.w
if w != 0:
x /= w
y /= w
z /= w
return vectors.Vector3d(x, y, z)
return Vector3d(x, y, z)
def get_projection_matrix(fov_degrees, aspect_ratio, near_plane, far_plane):
fov_rad = 1 / math.tan(fov_degrees * 0.5 / 180.0 * math.pi)
row1 = Vector4d(aspect_ratio * fov_rad, 0, 0, 0)
row2 = Vector4d(0, fov_rad, 0, 0)
row3 = Vector4d(0, 0, far_plane / (far_plane - near_plane), 1.0)
row4 = Vector4d(0, 0, -far_plane * near_plane / (far_plane - near_plane), 0)
return Matrix4x4(row1, row2, row3, row4)
def get_identity_matrix():
row1 = Vector4d(1, 0, 0, 0)
row2 = Vector4d(0, 1, 0, 0)
row3 = Vector4d(0, 0, 1, 0)
row4 = Vector4d(0, 0, 0, 1)
return Matrix4x4(row1, row2, row3, row4)
def get_y_rotation_matrix(angle_rad):
row1 = Vector4d(math.cos(angle_rad), 0, math.sin(angle_rad), 0)
row2 = Vector4d(0, 1, 0, 0)
row3 = Vector4d(-math.sin(angle_rad), 0, math.cos(angle_rad), 0)
row4 = Vector4d(0, 0, 0, 1)
return Matrix4x4(row1, row2, row3, row4)
def get_z_rotation_matrix(angle_rad):
row1 = Vector4d(math.cos(angle_rad), math.sin(angle_rad), 0, 0)
row2 = Vector4d(-math.sin(angle_rad), math.cos(angle_rad), 0, 0)
row3 = Vector4d(0, 0, 0, 0)
row4 = Vector4d(0, 0, 1, 0)
return Matrix4x4(row1, row2, row3, row4)
def get_x_rotation_matrix(angle_rad):
row1 = Vector4d(1, 0, 0, 0)
row2 = Vector4d(0, math.cos(angle_rad), math.sin(angle_rad), 0)
row3 = Vector4d(0, -math.sin(angle_rad), math.cos(angle_rad), 0)
row4 = Vector4d(0, 0, 0, 1)
return Matrix4x4(row1, row2, row3, row4)
class Matrix3x3:
def __init__(self, row0, row1, row2):
self.row0 = row0
def __init__(self, row1, row2, row3):
self.row1 = row1
self.row2 = row2
self.row3 = row3