DESIGN - Hardin and Sloane Spherical Designs

DESIGN implements a number of Hardin and Sloane spherical designs.

A set of N points which lie on the sphere is called a spherical T-design if the integral on the surface of the sphere of any polynomial of degree at most T is equal to the average value of the polynomial evaluated at the set of points. Note that the degree of a polynomial is the highest degree of any of its terms, and that the degree of a term like X^AY^BZ^C is A+B+C.

Reference 1:

R H Hardin and N J A Sloane,
McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions,
Discrete and Computational Geometry,
Volume 15, 1996, pages 429-441.

Reference 2:

Sloane's Spherical Designs Web Page

Files you may copy include:

• design, the source code.
• design_prb.f90, a sample problem.
• design_prb.out, sample problem output.

The list of routines includes:

• DESIGN_00_001_3D returns a 0-design of 1 point in 3D.
• DESIGN_01_002_3D returns a 1-design of 2 points in 3D.
• DESIGN_02_004_3D returns a 2-design of 4 points in 3D.
• DESIGN_03_006_3D returns a 3-design of 6 points in 3D.
• DESIGN_04_014_3D returns a 4-design of 14 points in 3D.
• DESIGN_05_012_3D returns a 5-design of 12 points in 3D.
• DESIGN_06_026_3D returns a 6-design of 26 points in 3D.
• DESIGN_07_024_3D returns a 7-design of 24 points in 3D.
• DESIGN_08_036_3D returns an 8-design of 36 points in 3D.
• DESIGN_09_048_3D returns a 9-design of 48 points in 3D.
• DESIGN_10_060_3D returns a 10-design of 60 points in 3D.
• DESIGN_11_070_3D returns an 11-design of 70 points in 3D.
• DESIGN_12_084_3D returns a 12-design of 84 points in 3D.
• DESIGN_13_094_3D returns a 13-design of 94 points in 3D.
• DESIGN_14_108_3D returns a 14-design of 108 points in 3D.
• DESIGN_15_120_3D returns a 15-design of 120 points in 3D.
• DESIGN_16_144_3D returns a 16-design of 144 points in 3D.
• DESIGN_17_156_3D returns a 17-design of 156 points in 3D.
• DESIGN_18_180_3D returns an 18-design of 180 points in 3D.
• DESIGN_19_204_3D returns a 19-design of 204 points in 3D.
• DESIGN_20_216_3D returns a 20-design of 216 points in 3D.
• DESIGN_21_240_3D returns a 21-design of 240 points in 3D.
• DESIGN_ORDER_MAX returns the maximum design order.
• DESIGN_POINTS returns the points for a given design.
• DESIGN_QUAD approximates an integral with a design of a given order.
• DESIGN_SIZE returns the size N of a design of a given order.
• GAMMA returns the value of the Gamma function at X.
• GAMMA_LOG calculates the natural logarithm of GAMMA ( X ) for positive X.
• R_PI returns the value of pi.
• S_CAT concatenates two strings to make a third string.
• SPHERE_AREA_3D computes the surface area of a sphere in 3D.
• SPHERE_MONOMIAL_INT_3D integrates a monomial on a sphere in 3D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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