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Catmull–Clark surfaces are defined recursively, using the following refinement scheme. [1] Start with a mesh of an arbitrary polyhedron. All the vertices in this mesh shall be called original points. For each face, add a face point. Set each face point to be the average of all original points for the respective face Face points (blue spheres)
Most recursive definitions have two foundations: a base case (basis) and an inductive clause. The difference between a circular definition and a recursive definition is that a recursive definition must always have base cases, cases that satisfy the definition without being defined in terms of the definition itself, and that all other instances in the inductive clauses must be "smaller" in some ...
A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...
Recursive data structures can dynamically grow to a theoretically infinite size in response to runtime requirements; in contrast, the size of a static array must be set at compile time. "Recursive algorithms are particularly appropriate when the underlying problem or the data to be treated are defined in recursive terms." [27]
This mutually recursive definition can be converted to a singly recursive definition by inlining the definition of a forest: t: v [t[1], ..., t[k]] A tree t consists of a pair of a value v and a list of trees (its children). This definition is more compact, but somewhat messier: a tree consists of a pair of one type and a list another, which ...
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Blue is the range of Felinae (excluding the domestic cat), green is the range of Pantherinae. Felidae is a family of mammals in the order Carnivora, colloquially referred to as cats. A member of this family is called a felid. [1] [2] The term "cat" refers both to felids in general and specifically to domestic cats.
Cats typically only knead soft surfaces such as a blanket, pillow, carpet, couch, or their owners. However, some cats reflexively “march” on a hard surface instead.