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64 lines
2.2 KiB
64 lines
2.2 KiB
11 months ago
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import numpy as np
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def project_point(camera_position, look_at, point_3d):
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"""
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Project a 3D point into a normalized projection matrix.
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Args:
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camera_position: The 3D position of the camera (x, y, z).
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look_at: The 3D position the camera is looking at (x, y, z).
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point_3d: The 3D point to project (x, y, z).
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Returns:
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The 2D coordinates of the projected point in normalized space.
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"""
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# Step 1: Calculate the forward, right, and up vectors
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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(camera_position))
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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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# Step 2: Create the view matrix
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view_matrix = np.array([
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[right[0], right[1], right[2], -np.dot(right, camera_position)],
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[up[0], up[1], up[2], -np.dot(up, camera_position)],
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[-forward[0], -forward[1], -forward[2], np.dot(forward, camera_position)],
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[0, 0, 0, 1]
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])
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# Step 3: Create the projection matrix
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near = 1.0 # Near plane normalized to 1
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width = 1.0 # Width of the near plane
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height = 1.0 # Height of the near plane
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aspect_ratio = width / height
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projection_matrix = np.array([
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[1 / aspect_ratio, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, -1, -2 * near],
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[0, 0, -1, 0]
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])
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# Step 4: Transform the 3D point into clip space
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point_3d_homogeneous = np.array([point_3d[0], point_3d[1], point_3d[2], 1])
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view_space_point = view_matrix @ point_3d_homogeneous
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clip_space_point = projection_matrix @ view_space_point
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# Step 5: Perform perspective divide to get normalized device coordinates (NDC)
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if clip_space_point[3] == 0:
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raise ValueError("Invalid projection: w component is zero.")
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ndc_x = clip_space_point[0] / clip_space_point[3]
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ndc_y = clip_space_point[1] / clip_space_point[3]
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return ndc_x, ndc_y
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# Example usage
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camera_position = (0, 0, 0) # Camera position
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look_at = (0, 0, -1) # Camera is looking along the negative Z-axis
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point_3d = (0.5, 0.5, -2) # A 3D point to project
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projected_point = project_point(camera_position, look_at, point_3d)
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print("Projected 2D Point in NDC:", projected_point)
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