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** Up:** The Fixed Viewpoint Constraint
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The first step in the solution of the fixed viewpoint constraint
equation is to solve it as a quadratic to yield an expression
for the surface slope:
| |
(9) |

The next step is to substitute and set
which yields:
| |
(10) |

Then, we substitute 2 *r x* = *y*^{2} + *r*^{2} - *b*^{2}, which when
differentiated gives:
| |
(11) |

and so we have:
| |
(12) |

Rearranging this equation yields:
| |
(13) |

Integrating both sides with respect to *r* results in:
| |
(14) |

where *C* is the constant of integration.
Hence,
| |
(15) |

where *k* = 2 *e*^{C} > 0 is a constant. By back substituting,
rearranging, and simplifying we arrive at the two equations which comprise
the general solution of the fixed viewpoint constraint equation:

In the first of these two equations, the constant parameter *k* is
constrained by (rather than *k*>0) since 0 < *k* < 2 leads
to complex solutions.

** Next:** Specific Solutions of the
** Up:** The Fixed Viewpoint Constraint
** Previous:** Derivation of the Fixed
*Simon Baker*

*1/22/1998*