TETRAHEDRON_PROPERTIES
Compute Properties of a Tetrahedron

TETRAHEDRON_PROPERTIES is a C++ program which computes properties of a tetrahedron.

These properties include:

• Centroid;
• Circumsphere (center and radius);
• Dihedral angles;
• Edge lengths;
• Face angles;
• Face areas;
• Insphere (center and radius);
• Quality1: ratio of insphere radius / circumsphere radius;
• Quality2: ratio of insphere radius / longest edge;
• Quality3: ratio of volume^(2/3) / sum of squares of edge lengths;
• Quality4: sine of half the minimum solid angle;
• Solid angles;
• Volume;

Usage:

tetrahedron_properties filename

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

GEOMETRY is a C++ library which performs geometric calculations in 2, 3 and N dimensional space.

TETRAHEDRON_PROPERTIES is available in a C++ version and a FORTRAN90 version and a MATLAB version.

TETRAHEDRONS, a dataset directory which contains examples of tetrahedrons;

Source Code:

• tetrahedron_properties.C, the source code.
• tetrahedron_properties.csh, commands to compile the source code.

Examples and Tests:

• tet_cap.txt, a "cap" tetrahedron.
• tet_cap_output.txt, the output file.
• tet_equilateral.txt, an equilateral tetrahedron.
• tet_equilateral_output.txt, the output file.
• tet_needle.txt, a "needle" tetrahedron.
• tet_needle_output.txt, the output file.
• tet_right.txt, a right tetrahedron.
• tet_right_output.txt, the output file.
• tet_sliver.txt, a "sliver" tetrahedron.
• tet_sliver_output.txt, the output file.
• tet_spindle.txt, a "spindle" tetrahedron.
• tet_spindle_output.txt, the output file.
• tet_wedge.txt, a "wedge" tetrahedron.
• tet_wedge_output.txt, the output file.

List of Routines:

• MAIN is the main program for TETRAHEDRON_PROPERTIES.
• ARC_COSINE computes the arc cosine function, with argument truncation.
• CH_CAP capitalizes a single character.
• CH_EQI is true if two characters are equal, disregarding case.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DTABLE_DATA_READ reads the data from a DTABLE file.
• DTABLE_HEADER_READ reads the header from a DTABLE file.
• FILE_COLUMN_COUNT counts the columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the minimum of two I4's.
• R8_ABS returns the absolute value of an R8.
• R8_HUGE returns a "huge" R8.
• R8_MAX returns the maximum of two R8's.
• R8_MIN returns the minimum of two R8's.
• R8_SWAP switches two R8's.
• R8MAT_DET_4D computes the determinant of a 4 by 4 R8MAT.
• R8MAT_SOLVE uses Gauss-Jordan elimination to solve an N by N linear system.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8VEC_ANGLE_3D computes the angle between two vectors in 3D.
• R8VEC_CROSS_3D computes the cross product of two R8VEC's in 3D.
• R8VEC_DOT computes the dot product of a pair of R8VEC's in ND.
• R8VEC_LENGTH returns the Euclidean length of an R8VEC.
• R8VEC_MAX returns the value of the maximum element in an R8VEC.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_ZERO zeroes an R8VEC.
• S_LEN_TRIM returns the length of a string to the last nonblank.
• S_TO_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• TETRAHEDRON_CENTROID_3D computes the centroid of a tetrahedron in 3D.
• TETRAHEDRON_CIRCUMSPHERE_3D computes the circumsphere of a tetrahedron in 3D.
• TETRAHEDRON_DIHEDRAL_ANGLES_3D computes dihedral angles of a tetrahedron.
• TETRAHEDRON_EDGE_LENGTH_3D returns edge lengths of a tetrahedron in 3D.
• TETRAHEDRON_FACE_ANGLES_3D returns the 12 face angles of a tetrahedron 3D.
• TETRAHEDRON_FACE_AREAS_3D returns the 4 face areas of a tetrahedron 3D.
• TETRAHEDRON_INSPHERE_3D finds the insphere of a tetrahedron in 3D.
• TETRAHEDRON_QUALITY1_3D: "quality" of a tetrahedron in 3D.
• TETRAHEDRON_QUALITY2_3D: "quality" of a tetrahedron in 3D.
• TETRAHEDRON_QUALITY3_3D computes the mean ratio of a tetrahedron.
• TETRAHEDRON_QUALITY4_3D computes the minimum solid angle of a tetrahedron.
• TETRAHEDRON_SOLID_ANGLES_3D computes solid angles of a tetrahedron.
• TETRAHEDRON_VOLUME_3D computes the volume of a tetrahedron in 3D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_ANGLES_3D computes the angles of a triangle in 3D.
• TRIANGLE_AREA_3D computes the area of a triangle in 3D.

You can go up one level to the C++ source codes.