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import math
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import numpy as np,array
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def project_3d_to_2d(square_3d, observer, look_at, fov=90, aspect_ratio=1, near=0.1, far=1000):
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"""
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Project a 3D square onto a 2D plane.
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Args:
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square_3d: List of 4 points representing the square in 3D space [(x, y, z), ...].
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observer: The observer's position in 3D space (x, y, z).
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look_at: The point the observer is looking at in 3D space (x, y, z).
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fov: Field of view in degrees.
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aspect_ratio: Aspect ratio of the 2D plane (width/height).
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near: Near clipping plane.
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far: Far clipping plane.
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Returns:
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List of 2D points [(x, y), ...].
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"""
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# Step 1: Create the view matrix
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def normalize(v):
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return v / np.linalg.norm(v)
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forward = normalize(np.array(look_at) - np.array(observer))
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right = normalize(np.cross(forward, [0, 1, 0]))
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up = np.cross(right, forward)
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view_matrix = np.array([
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[right[0], right[1], right[2], -np.dot(right, observer)],
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[up[0], up[1], up[2], -np.dot(up, observer)],
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[-forward[0], -forward[1], -forward[2], np.dot(forward, observer)],
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[0, 0, 0, 1]
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])
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# Step 2: Create the projection matrix
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fov_rad = np.radians(fov)
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f = 1 / np.tan(fov_rad / 2)
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projection_matrix = np.array([
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[f / aspect_ratio, 0, 0, 0],
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[0, f, 0, 0],
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[0, 0, (far + near) / (near - far), (2 * far * near) / (near - far)],
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[0, 0, -1, 0]
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])
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# Step 3: Transform the 3D points to 2D
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square_2d = []
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for point in square_3d:
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# Convert to homogeneous coordinates
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point_3d = np.array([point[0], point[1], point[2], 1])
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# Apply view and projection transformations
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transformed_point = projection_matrix @ view_matrix @ point_3d
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# Perform perspective divide
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x = transformed_point[0] / transformed_point[3]
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y = transformed_point[1] / transformed_point[3]
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square_2d.append((x, y))
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return square_2d
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# Example usage
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square_3d = [
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(1, 1, 5), # Top-right
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(-1, 1, 5), # Top-left
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(-1, -1, 5), # Bottom-left
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(1, -1, 5) # Bottom-right
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]
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observer = (0, 0, 0) # Observer's position
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look_at = (0, 0, 1) # Observer is looking along the positive Z-axis
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square_2d = project_3d_to_2d(square_3d, observer, look_at)
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print("2D Coordinates of the square:", square_2d)
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