Changed matrix object names to be more natural. Fixed a bug in the matrix projection math.
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@@ -10,7 +10,7 @@ ui = window.Window(600, 600)
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near_plane = 0.1
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far_plane = 1000.0
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fov = 90.0
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#'''
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tris =[
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Matrix3x3(Vector3d(0.0,0.0,0.0),Vector3d(0.0,1.0,0.0),Vector3d(1.0,1.0,0.0)),
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Matrix3x3(Vector3d(0.0,0.0,0.0),Vector3d(1.0,1.0,0.0),Vector3d(1.0,0.0,0.0)),
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@@ -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)),
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Matrix3x3(Vector3d(1.0,0.0,1.0),Vector3d(0.0,0.0,1.0),Vector3d(0.0,0.0,0.0)),
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Matrix3x3(Vector3d(1.0,0.0,1.0),Vector3d(0.0,0.0,0.0),Vector3d(1.0,0.0,0.0))
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]
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#'''
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#tris = Mesh()
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def main():
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#tris.load_obj_file('shuttle.obj')
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#tris.load_obj_file('teddy.obj')
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ui.thetax = 1
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ui.thetay = 1
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ui.window.bind('<Left>', left)
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ui.window.bind('<Right>', right)
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ui.window.bind('<Up>', up)
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ui.window.bind('<Down>', down)
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ui.window.bind('<ButtonPress-1>', mouse_start)
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ui.canvas.bind('<B1-Motion>', mouse_end)
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ui.canvas.old_coords = None
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@@ -40,27 +42,35 @@ def main():
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ui.show()
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def left(event):
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ui.theta -= .01
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ui.thetax -= .1
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draw_scene()
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def right(event):
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ui.theta += .01
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ui.thetax += .1
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draw_scene()
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def up(event):
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ui.thetay += .1
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draw_scene()
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def down(event):
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ui.thetay -= .1
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draw_scene()
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def mouse_start(event):
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ui.canvas.old_coords = event.x, event.y
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def mouse_end(event):
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x, y = ui.canvas.old_coords[0] - event.x, ui.canvas.old_coords[1] - event.y
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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
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if x < 0:
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ui.theta += .01
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ui.thetax -= .01
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else:
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ui.theta -= .01
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print(ui.theta)
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ui.thetax += .01
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if y < 0:
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ui.thetax += .01
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ui.thetay -= .01
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else:
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ui.thetax -= .01
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ui.thetay += .01
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draw_scene()
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#ui.theta += x / ui.width
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@@ -69,109 +79,97 @@ def draw_scene():
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ui.canvas.delete("all")
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#ui.theta += .01 # scaling factor
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aspect_ratio = ui.height / ui.width
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fov_rad = ui.theta / math.tan(fov * 0.5 / 180.0 * math.pi)
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projection_matrix = Matrix4x4.get_projection_matrix(fov, aspect_ratio, near_plane, far_plane)
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row0 = Vector4d(aspect_ratio * fov_rad, 0, 0, 0)
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row1 = Vector4d(0, fov_rad, 0, 0)
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row2 = Vector4d(0, 0, far_plane / (far_plane - near_plane), 1.0)
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row3 = Vector4d(0, 0, -far_plane * near_plane / (far_plane - near_plane), 0)
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rotation_matrix_y = Matrix4x4.get_y_rotation_matrix(ui.thetax)
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projection_matrix = Matrix4x4(row0, row1, row2, row3)
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row0 = Vector4d(math.cos(ui.theta), math.sin(ui.theta), 0, 0)
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row1 = Vector4d(-math.sin(ui.theta), math.cos(ui.theta), 0, 0)
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row2 = Vector4d(0, 0, 1, 0)
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row3 = Vector4d(0, 0, 0, 1)
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rotation_matrix_z = Matrix4x4(row0, row1, row2, row3)
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row0 = Vector4d(1, 0, 0, 0)
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row1 = Vector4d(0, math.cos(ui.thetax * 0.5), math.sin(ui.thetax * 0.5), 0)
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row2 = Vector4d(0, -math.sin(ui.thetax * 0.5), math.cos(ui.thetax * 0.5), 0)
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row3 = Vector4d(0, 0, 0, 1)
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rotation_matrix_x = Matrix4x4(row0, row1, row2, row3)
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rotation_matrix_x = Matrix4x4.get_x_rotation_matrix(ui.thetay)
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triangles = []
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for tri in tris:
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# Rotate on the z-axis
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row0 = rotation_matrix_z.multiply_3d(tri.row0)
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row1 = rotation_matrix_z.multiply_3d(tri.row1)
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row2 = rotation_matrix_z.multiply_3d(tri.row2)
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row1 = rotation_matrix_y.multiply_3d(tri.row1)
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row2 = rotation_matrix_y.multiply_3d(tri.row2)
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row3 = rotation_matrix_y.multiply_3d(tri.row3)
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rotated_z = Matrix3x3(row0, row1, row2)
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rotated_y = Matrix3x3(row1, row2, row3)
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# Rotate on the x-axis
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row0 = rotation_matrix_x.multiply_3d(rotated_z.row0)
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row1 = rotation_matrix_x.multiply_3d(rotated_z.row1)
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row2 = rotation_matrix_x.multiply_3d(rotated_z.row2)
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row1 = rotation_matrix_x.multiply_3d(rotated_y.row1)
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row2 = rotation_matrix_x.multiply_3d(rotated_y.row2)
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row3 = rotation_matrix_x.multiply_3d(rotated_y.row3)
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rotated_x = Matrix3x3(row0, row1, row2)
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rotated_x = Matrix3x3(row1, row2, row3)
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# The offset into the screen
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translated = copy.copy(rotated_x)
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translated.row0.z += 3.0
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translated.row1.z += 3.0
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translated.row2.z += 3.0
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translated.row3.z += 3.0
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# Use cross-product to get the surface normal (a Vector3d)
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x = translated.row1.x - translated.row0.x
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y = translated.row1.y - translated.row0.y
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z = translated.row1.z - translated.row0.z
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x = translated.row2.x - translated.row1.x
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y = translated.row2.y - translated.row1.y
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z = translated.row2.z - translated.row1.z
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line1 = Vector3d(x, y, z)
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x = translated.row2.x - translated.row0.x
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y = translated.row2.y - translated.row0.y
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z = translated.row2.z - translated.row0.z
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x = translated.row3.x - translated.row1.x
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y = translated.row3.y - translated.row1.y
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z = translated.row3.z - translated.row1.z
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line2 = Vector3d(x, y, z)
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normal = line1.cross_product(line2)
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# Now we normalize the normal
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w = math.sqrt(normal.x * normal.x + normal.y * normal.y + normal.z * normal.z)
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normal.x /= w
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normal.y /= w
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normal.z /= w
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length = math.sqrt(normal.x * normal.x + normal.y * normal.y + normal.z * normal.z)
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normal.x /= length
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normal.y /= length
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normal.z /= length
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# Do we display this triangle?
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if normal.dot_product(translated.row0) < 0.0:
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if normal.dot_product(translated.row1) < 0.0:
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# Lighting
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light = Vector3d(0, 0, -1) # Shining at the player.
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w = math.sqrt(light.x * light.x + light.y * light.y + light.z * light.z)
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light.x /= w
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light.y /= w
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light.z /= w
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length = math.sqrt(light.x * light.x + light.y * light.y + light.z * light.z)
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light.x /= length
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light.y /= length
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light.z /= length
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dot_product = normal.dot_product(light)
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r = abs(int(255 * dot_product))
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# Scale into view
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row0 = projection_matrix.multiply_3d(translated.row0)
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row1 = projection_matrix.multiply_3d(translated.row1)
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row2 = projection_matrix.multiply_3d(translated.row2)
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row2 = projection_matrix.multiply_3d(translated.row2)
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row3 = projection_matrix.multiply_3d(translated.row3)
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projected = Matrix3x3(row0, row1, row2)
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projected = Matrix3x3(row1, row2, row3)
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projected.row0.x += 1
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projected.row0.y += 1
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projected.row1.x += 1
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projected.row1.y += 1
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projected.row2.x += 1
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projected.row2.y += 1
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projected.row0.x *= .5 * ui.width
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projected.row0.y *= .5 * ui.height
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projected.row3.x += 1
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projected.row3.y += 1
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projected.row1.x *= .5 * ui.width
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projected.row1.y *= .5 * ui.height
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projected.row2.x *= .5 * ui.width
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projected.row2.x *= .5 * ui.width
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projected.row2.y *= .5 * ui.height
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projected.row3.x *= .5 * ui.width
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projected.row3.y *= .5 * ui.height
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t = Triangle(projected)
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t.color = r
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t.average = (t.coords.row1.z + t.coords.row2.z + t.coords.row3.z) / 3
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triangles.append(t)
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# Sort the triangles so they are drawn in order.
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triangles.sort(key=lambda r: r.average, reverse = True)
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for projected in triangles:
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r = projected.color
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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]
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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]
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ui.canvas.create_polygon(coords, fill=from_rgb(r, r, r), outline="black")
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ui.canvas.update()
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