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74 lines
2.7 KiB
74 lines
2.7 KiB
10 months ago
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import math
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def project_3d_to_2d(observer, look_at, fov_h, fov_v, screen_width, screen_height, point_3d):
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"""
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Project a 3D point onto a 2D screen.
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Args:
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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_h: Horizontal field of view in radians.
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fov_v: Vertical field of view in radians.
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screen_width: Width of the 2D screen.
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screen_height: Height of the 2D screen.
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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 (x, y) on the screen.
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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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length = math.sqrt(sum(coord ** 2 for coord in v))
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return tuple(coord / length for coord in v)
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forward = normalize((look_at[0] - observer[0], look_at[1] - observer[1], look_at[2] - observer[2]))
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right = normalize((
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forward[1] * 0 - forward[2] * 1,
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forward[2] * 0 - forward[0] * 0,
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forward[0] * 1 - forward[1] * 0
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))
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up = (
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right[1] * forward[2] - right[2] * forward[1],
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right[2] * forward[0] - right[0] * forward[2],
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right[0] * forward[1] - right[1] * forward[0]
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)
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# Step 2: Transform the 3D point into the observer's coordinate system
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relative_point = (
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point_3d[0] - observer[0],
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point_3d[1] - observer[1],
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point_3d[2] - observer[2]
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)
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x_in_view = sum(relative_point[i] * right[i] for i in range(3))
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y_in_view = sum(relative_point[i] * up[i] for i in range(3))
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z_in_view = sum(relative_point[i] * forward[i] for i in range(3))
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# Step 3: Perform perspective projection
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if z_in_view <= 0:
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raise ValueError("The point is behind the observer and cannot be projected.")
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aspect_ratio = screen_width / screen_height
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tan_fov_h = math.tan(fov_h / 2)
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tan_fov_v = math.tan(fov_v / 2)
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ndc_x = x_in_view / (z_in_view * tan_fov_h * aspect_ratio)
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ndc_y = y_in_view / (z_in_view * tan_fov_v)
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# Step 4: Map normalized device coordinates (NDC) to screen coordinates
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screen_x = (ndc_x + 1) / 2 * screen_width
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screen_y = (1 - ndc_y) / 2 * screen_height
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return screen_x, screen_y
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# Example usage
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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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fov_h = math.radians(90) # Horizontal FOV in radians
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fov_v = math.radians(60) # Vertical FOV in radians
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screen_width = 800 # Screen width
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screen_height = 600 # Screen height
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point_3d = (1, 1, 5) # The 3D point to project
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projected_2d_point = project_3d_to_2d(observer, look_at, fov_h, fov_v, screen_width, screen_height, point_3d)
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print("Projected 2D Point:", projected_2d_point)
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