| 单词 | parameterized surface |
| 释义 | parameterized surface • r is a continuous (see continuous function) bijection from U onto X and r−1 is continuous; that is, r is a homeomorphism between U and X; • ∂r/∂x, ∂r/∂y exist and are continuous; • (smoothness condition) ∂r/∂x and ∂r/∂y are linearly independent. The last condition means that the tangent vectors ∂r/∂x and ∂r/∂y span a 2-dimensional vector space called the tangent space. The smooth condition is equivalent to EG–F2 ≠ 0, where E,2F,G are the coefficients of the first fundamental form. See also atlas, transition map. |
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