Golf ball dimples defined by superposed curves
The present invention is a golf ball which comprises dimples having a cross-sectional shape defined by the superposition of a weighted profile and one or more additional profiles, and a method of making such dimples. The dimples preferably have a circular boundary and maintain an axis coincident with the center of the circular boundary.
1. A golf ball having a plurality of recessed dimples on the surface thereof, wherein at least a portion of the recessed dimples have a non-spherical cross-sectional profile defined by a function ƒ(x) resulting from the sum of a weighted function and one or more additional functions g(x), wherein the weighted function is the multiplication of a single continuous, differentiable function b(x) and at least one weighting function w(x) selected from the group consisting of polynomial, exponential, and trigonometric functions, such that the function defining the cross-sectional profile is expressed as
ƒ( x )=( b ( x )* w ( x ))+ g ( x ).
2. The golf ball of claim 1 , wherein g(x) is a spherical function.
3. The golf ball of claim 1 , wherein g(x) is a conical function.
4. The golf ball of claim 1 , wherein g(x) is a catenary function.
5. The golf ball of claim 1 , wherein g(x) is an elliptical function.
6. The golf ball of claim 1 , wherein g(x) is a polynomial function.
7. The golf ball of claim 1 , wherein g(x) is a trigonometric function.
8. The golf ball of claim 1 , wherein b(x) is selected from the group consisting of spherical, conical, catenary, elliptical, polynomial, and trigonometric functions.
9. The golf ball of claim 1 , wherein b(x) is selected from the group consisting of Witch of Agnesi, frequency, Neiles parabola, and trigonometric functions.
10. The golf ball of claim 1 , wherein ƒ(x) is a continuous and differentiable function.
11. The golf ball of claim 1 , wherein b(x) is a spherical function.