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Video Game Design Foundations
Mathematics
4. To wrap a texture around an object, the image has to be cut or stretched.
Use a round object like a tennis ball to represent a UV sphere.
A. Wrap a rectangular piece of paper around the ball. The bottom edge of
the paper should follow the equator (middle of the ball).
B. Bend one point on the top of the paper so it just touches the north pole
of the ball. Mark that point and then cut off the top of the paper all the
way around at that point.
C. Measure the length of the equator.
D. Measure the height of the paper from the north pole to the equator.
E. Use this formula to determine the area of the rectangle formed by the
paper:
base × height = area of rectangle
F. Every 1″, cut from the top of the paper to the bottom. Leave about 1/8″
uncut so the paper stays in one piece.
G. Lay down each segment over the top of the ball. Draw a line to show the
overlap between segments.
H. Cut out along the overlap lines to get the paper to lay flat without
overlapping.
I. When you have the ball covered, unwrap the paper and examine
how triangles were formed when you cut out the curves. Measure the
triangular sections. Use this formula to determine the area of each
triangle.
1/2 base × height = area of triangle
Note: The sections are not true triangles because the edges are curved,
not straight, but this formula will provide an approximation of the area.
J. Add the total area of the removed triangles. Determine what percentage
of the paper was removed in the wrapping.