3D SCALING
The matrix expression tor the scaling transformation of an edge P = (x, y, z) relative to the coordinate origin will be written as
Where scaling parameters sx, sy, and sz, are assigned any positive values. Explicit expressions for the coordinate transformations for scaling relative to the origin are
x' = x . sx,
y' = y . sy,
z' = z. sz
Scaling an object with transformation changes the dimensions of the article and repositions the article relative to the coordinate origin. Also, if the transformation parameters don't seem to be all equal, relative dimensions within the object are changed. We preserve the initial shape of an object with the same scaling (s, = s, = s,). The results of scaling an object uniformly with each scaling parameter set to 2. Scaling with relevancy a specific fixed position (xf, yf, zf,) will be represented with the
subsequent transformation sequence:
1. Translate the fixed point to the origin.
2. Scale the article relative to the coordinate origin.
3. Translate the fixed point back to its original position.
The matrix representation for an arbitrary fixed-point scaling can then be expressed because the concatenation of those translate-scale-translate transformations as
We form the inverse scaling matrix for the equation by re-equivalent to the sequence of placing the scaling parameters sx, sy, and sz with their reciprocals. The inverse matrix generates an opposite scaling transformation, therefore the concatenation of any scaling matrix and its inverse produces the unit matrix.
Where scaling parameters sx, sy, and sz, are assigned any positive values. Explicit expressions for the coordinate transformations for scaling relative to the origin are
x' = x . sx,
y' = y . sy,
z' = z. sz
Scaling an object with transformation changes the dimensions of the article and repositions the article relative to the coordinate origin. Also, if the transformation parameters don't seem to be all equal, relative dimensions within the object are changed. We preserve the initial shape of an object with the same scaling (s, = s, = s,). The results of scaling an object uniformly with each scaling parameter set to 2. Scaling with relevancy a specific fixed position (xf, yf, zf,) will be represented with the
subsequent transformation sequence:
1. Translate the fixed point to the origin.
2. Scale the article relative to the coordinate origin.
3. Translate the fixed point back to its original position.
The matrix representation for an arbitrary fixed-point scaling can then be expressed because the concatenation of those translate-scale-translate transformations as
We form the inverse scaling matrix for the equation by re-equivalent to the sequence of placing the scaling parameters sx, sy, and sz with their reciprocals. The inverse matrix generates an opposite scaling transformation, therefore the concatenation of any scaling matrix and its inverse produces the unit matrix.
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