I was recently inspired to make a simple 3D engine in python, but upon doing a little research I concluded it was too advanced for my skill level (I'm self taught and pretty new to python), but I decided to try it anyway. After a couple of days I was able to make what looks to me like an accurate 3D engine using only trig, no matrices or vectors.
My method is to extend a plane from the camera down the y-axis, and the plane will grow the further away it is from the origin. If the plane intersects a point, the coordinates of said point will be rescaled to the size of the screen I'm projecting the point onto. Rather than changing the direction that the plane extends I rotate the points around the camera to make it seem as if the camera is looking in a different direction. I do a similar thing for moving the points, rather than moving the camera I move the points around the camera.
Is this an accurate representation of 3D space, or is do you need vectors and matrices to make that?
Here's my code:
import pygame
import math
pygame.init()
screen = pygame.display.set_mode((2000,1300))
pygame.display.set_caption("3D Engine")
cube = [[0, 200, 0], [0, 250, 0], [50, 250, 0], [50, 200, 0], [50, 250, 50], [50, 200, 50], [0, 250, 50], [0, 200, 50]]
camera_pos = [0, 0, 0]
camera_angle = [00, 0]
clock = pygame.time.Clock()
esc = False
render_list = []
def get_angle_flat(p):
a = 69
if p[0] > 0:
if p[1] > 0:
quad = 1
elif p[1] < 0:
quad = 4
else:
a = 0
elif p[0] < 0:
if p[1] > 0:
quad = 2
elif p[1] < 0:
quad = 3
else:
a = math.pi
else:
if p[1] > 0:
a = math.pi/2
elif p[1] < 0:
a = -math.pi/2
else:
a = "null"
if a != 0 and a != math.pi and a != math.pi/2 and a != -math.pi/2:
if quad == 1:
a = math.atan(p[1]/p[0])
elif quad == 2:
a = math.pi+math.atan(p[1]/p[0])
elif quad == 3:
a = -(math.pi-math.atan(p[1]/p[0]))
elif quad == 4:
a = math.atan(p[1]/p[0])
return a
def get_angle_side(p):
a = 2
if p[1] > 0:
if p[2] > 0:
quad = 1
elif p[2] < 0:
quad = 4
else:
a = 0
elif p[1] < 0:
if p[2] > 0:
quad = 2
elif p[2] < 0:
quad = 3
else:
a = math.pi
else:
if p[2] > 0:
a = math.pi/2
elif p[2] < 0:
a = -math.pi/2
else:
a = "null"
if a != 0 and a != math.pi and a != math.pi/2 and a != -math.pi/2:
if quad == 1:
a = math.atan(p[2]/p[1])
elif quad == 2:
a = math.pi+math.atan(p[2]/p[1])
elif quad == 3:
a = -(math.pi-math.atan(p[2]/p[1]))
elif quad == 4:
a = math.atan(p[2]/p[1])
return a
def to_degrees(a):
return a*180/math.pi
def distance(p):
dis = math.sqrt(pow(p[0], 2) + pow(p[1], 2))
return dis
def distance_2(p):
dis = math.sqrt(pow(p[1], 2) + pow(p[2], 2))
return dis
def to_radians(a):
return a/180*math.pi
while True:
render_list = []
if not esc:
pygame.mouse.set_pos((1000, 650))
pygame.mouse.set_visible(False)
else:
pygame.mouse.set_visible(True)
screen.fill((0, 0, 0))
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
break
pressed = pygame.key.get_pressed()
if pressed[pygame.K_w]:
for item in cube:
item[1] -= 1
if pressed[pygame.K_a]:
for item in cube:
item[0] += 1
if pressed[pygame.K_s]:
for item in cube:
item[1] += 1
if pressed[pygame.K_d]:
for item in cube:
item[0] -= 1
if pressed[pygame.K_SPACE]:
for item in cube:
item[2] += 1
if pressed[pygame.K_LSHIFT]:
for item in cube:
item[2] -= 1
if pressed[pygame.K_ESCAPE]:
esc = not esc
mouse_pos = pygame.mouse.get_pos()
mouse_pos = list(mouse_pos)
mouse_pos[0] = 1000 - mouse_pos[0]
mouse_pos[1] = 650 - mouse_pos[1]
print(math.cos(to_radians(camera_angle[0])))
past_c_a = camera_angle.copy()
if not esc:
camera_angle[0] += mouse_pos[0]/3
camera_angle[1] -= mouse_pos[1]/3
if camera_angle[0] > 360:
camera_angle[0] = 0
elif camera_angle[0] < 0:
camera_angle[0] = 360
if camera_angle[1] > 360:
camera_angle[1] = 0
elif camera_angle[1] < 0:
camera_angle[1] = 360
if camera_angle != past_c_a:
for i in range(len(cube)):
dist = distance(cube[i])
cube[i] = [math.cos(to_radians(to_degrees(get_angle_flat(cube[i])) + (past_c_a[0]-camera_angle[0])))*dist, math.sin(to_radians(to_degrees(get_angle_flat(cube[i])) + (past_c_a[0]-camera_angle[0])))*dist, cube[i][-1]]
dist2 = distance_2(cube[i])
cube[i] = [cube[i][0], math.cos(to_radians(to_degrees(get_angle_side(cube[i])) + (past_c_a[1]-camera_angle[1])))*dist2, math.sin(to_radians(to_degrees(get_angle_side(cube[i])) + (past_c_a[1]-camera_angle[1])))*dist2]
for i in range(len(cube)):
if cube[i][1] > 0:
size = [cube[i][1]*5/2, cube[i][1]*3.25/2]
render_list.append([cube[i][0]*(2000/size[0])+1000, cube[i][2]*(1300/size[1])+650])
else:
render_list.append("null")
if "null" not in render_list:
pygame.draw.line(screen, (255, 255, 255), render_list[0], render_list[1], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[0], render_list[3], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[0], render_list[-1], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[1], render_list[-2], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[1], render_list[2], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[2], render_list[4], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[3], render_list[-3], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[4], render_list[-2], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[4], render_list[-3], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[7], render_list[-2], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[7], render_list[-3], 2)
pygame.draw.line(screen, (255, 255, 255), render_list[3], render_list[2], 2)
pygame.display.update()
clock.tick(120)
