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Michael Zhang 2023-04-30 16:03:33 -05:00
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x$ axis, its tail pointing upwards in the $+y$ direction and its nose facing x$ axis, its tail pointing upwards in the $+y$ direction and its nose facing
in the $+z$ direction. Derive a sequence of model transformation matrices in the $+z$ direction. Derive a sequence of model transformation matrices
that can be applied to the vertices of the airplane to position it in space that can be applied to the vertices of the airplane to position it in space
at the location $p = (4, 4, 7)$, with a direction of flight $w = (2, 1, –2)$ at the location $p = (4, 4, 7)$, with a direction of flight $w = (2, 1, -2)$
and the wings aligned with the direction $d = (–2, 2, –1)$.} and the wings aligned with the direction $d = (-2, 2, –1)$.}
The translation matrix is The translation matrix is
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transform it to $(2, 1, -2)$. transform it to $(2, 1, -2)$.
8. Consider the perspective projection-normalization matrix P which maps the 8. Consider the perspective projection-normalization matrix P which maps the
contents of the viewing frustum into a cube that extends from –1 to 1 in $x, contents of the viewing frustum into a cube that extends from -1 to 1 in $x,
y, z$ (called normalized device coordinates). y, z$ (called normalized device coordinates).
Suppose you want to define a square, symmetric viewing frustum with a near Suppose you want to define a square, symmetric viewing frustum with a near
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patch, it can be inefficient to separately represent each triangle in the patch, it can be inefficient to separately represent each triangle in the
patch independently as a set of three vertices because memory is wasted when patch independently as a set of three vertices because memory is wasted when
the same vertex location has to be specified multiple times. A triangle the same vertex location has to be specified multiple times. A triangle
strip offers a memory-efficient method for representing connected ‘strips’ strip offers a memory-efficient method for representing connected 'strips'
of triangles. For example, in the diagram below, the six vertices v0 .. v5 of triangles. For example, in the diagram below, the six vertices v0 .. v5
define four adjacent triangles: (v0, v1, v2), (v2, v1, v3), (v2, v3, v4), define four adjacent triangles: (v0, v1, v2), (v2, v1, v3), (v2, v3, v4),
(v4, v3, v5). [Notice that the vertex order is switched in every other (v4, v3, v5). [Notice that the vertex order is switched in every other