GEOMETRYC - Geometric Calculations

GEOMETRYC is a collection of routines for geometric calculations in 2, 3 and N space. These calculations include angles, areas, containment, distances, intersection, nearest point, and volumes. The objects considered include points, lines, line segments, polygons, planes, polyhedra and vectors.

GEOMETRYC is a C version of a subset of the FORTRAN GEOMETRY collection.

Reference 1:

Adrian Bowyer and John Woodwark,
A Programmer's Geometry,
Butterworths, 1983.

Reference 2:

Joseph O'Rourke,
Computational Geometry,
Cambridge University Press,
Second Edition, 1998.

Files you may copy include:

• geometryc.c, the source code;
• geometryc.h, the include file;
• geometryc_prb.c, the calling program;
• geometryc_prb.out, the sample output.

The list of routines includes:

• ANGLE_CONTAINS_RAY_2D determines if an angle contains a ray, in 2D.
• ANGLE_DEG_2D returns the angle in degrees between two rays in 2D.
• ANGLE_RAD_2D returns the angle in radians between two rays in 2D.
• ANGLE_RAD_3D returns the angle in radians between two vectors in 3D.
• ANGLE_RAD_ND returns the angle in radians between two vectors in ND.
• ANGLEI_DEG_2D returns the interior angle in degrees between two rays in 2D.
• ANGLEI_RAD_2D returns the interior angle in radians between two rays in 2D.
• ARC_COSINE computes the arc cosine function, with argument truncation.
• ATAN4 computes the inverse tangent of the ratio Y / X.
• BOX_CONTAINS_POINT_3D determines if a point is inside a parallelepiped in 3D.
• BOX_POINT_DIST_3D distance ( parallelepiped, point ) in 3D.
• CIRCLE_DIA2IMP_2D converts a diameter to an implicit circle in 2D.
• CIRCLE_EXP_CONTAINS_POINT_2D determines if an explicit circle contains a point in 2D.
• CIRCLE_IMP_CONTAINS_POINT_2D determines if an implicit circle contains a poin
• CIRCLE_IMP_LINE_PAR_INT_2D: ( implicit circle, parametric line ) intersection
• CIRCLE_POINTS_2D returns N equally spaced points on the circle in 2D.
• CONE_AREA_3D computes the surface area of a right circular cone in 3D.
• CONE_VOLUME_3D computes the volume of a right circular cone in 3D.
• COT returns the cotangent of an angle.
• COTD returns the cotangent of an angle given in degrees.
• CROSS_2D computes the cross product of two vectors in 2D.
• CROSS_3D computes the cross product of two vectors in 3D.
• CROSS0_2D computes the cross product of (P1-P0) and (P2-P0) in 2D.
• CROSS0_3D computes the cross product of (P1-P0) and (P2-P0) in 3D.
• DIRECTION_PERT_3D randomly perturbs a direction vector in 3D.
• DIRECTION_RANDOM_3D computes a random direction vector in 3D.
• DIRECTION_RANDOM_ND computes a random direction vector in ND.
• DOT_2D computes the dot product of a pair of vectors in 2D.
• DOT_3D computes the dot product of a pair of vectors in 3D.
• DOT_ND computes the dot product of a pair of vectors in ND.
• DOT0_2D computes the dot product of (P1-P0) and (P2-P0) in 2D.
• DOT0_3D computes the dot product of (P1-P0) and (P2-P0) in 3D.
• ENORM_2D computes the Euclidean norm of a vector in 2D.
• ENORM_3D computes the Euclidean norm of a vector in 3D.
• ENORM_ND computes the Euclidean norm of a vector in ND.
• ENORM0_2D computes the Euclidean norm of (P1-P0) in 2D.
• ENORM0_3D computes the Euclidean norm of (P1-P0) in 3D.
• ENORM0_ND computes the Euclidean norm of (P1-P0) in ND.
• ENORMSQ0_2D computes the squared Euclidean norm of (P1-P0) in 2D.
• ENORMSQ0_3D computes the squared Euclidean norm of (P1-P0) in 3D.
• ENORMSQ0_ND computes the squared Euclidean norm of (P1-P0) in ND.
• GET_SEED returns a random seed for the random number generator.
• HALFSPACE_IMP_TRIANGLE_INT_3D: intersection ( implicit halfspace, triangle ) in 3D.
• HALFSPACE_NORM_TRIANGLE_INT_3D: intersection ( normal halfspace, triangle ) in 3D.
• HALFSPACE_TRIANGLE_INT_3D: intersection ( halfspace, triangle ) in 3D.
• I_RANDOM returns a random integer in a given range.
• LINE_EXP_POINT_DIST_2D: distance ( explicit line, point ) in 2D.
• LINE_EXP_POINT_DIST_3D: distance ( explicit line, point ) in 3D.
• LINE_EXP_POINT_DIST_SIGNED_2D: signed distance ( explicit line, point ) in 2D.
• LINE_EXP2IMP_2D converts an explicit line to implicit form in 2D.
• LINE_EXP2PAR_3D converts a line from explicit to parametric form in 3D.
• LINE_SEG_POINT_DIST_3D computes the distance from a point to a line segment in 3D.
• LINE_SEG_POINT_NEAR_3D finds the point on a line segment nearest a point in 3D.
• LINES_IMP_ANGLE_2D finds the angle between two implicit lines in 2D.
• LINES_IMP_INT_2D finds where two implicit lines intersect in 2D.
• LINES_SEG_DIST_3D computes the distance between two line segments in 3D.
• MINQUAD finds a local minimum of F(X) = A * X**2 + B * X + C.
• NORMAL_01_SAMPLE returns random values from the standard 0,1 normal distribution.
• PARA_CONTAINS_POINT_3D determines if a point is inside a parallelogram in 3D.
• PARA_POINT_DIST_3D: distance ( parallelogram, point ) in 3D.
• PARABOLA_EX finds the extremal point of a parabola from 3 data points.
• PARABOLA_EX2 finds the extremal point of a parabola from 3 data points.
• PLANE_EXP_NORMAL_3D finds the normal to an explicit plane in 3D.
• PLANE_EXP2IMP_3D converts an explicit plane to implicit form in 3D.
• PLANE_EXP2NORM_3D converts an explicit plane to normal form in 3D.
• PLANE_IMP_LINE_SEG_NEAR_3D: distance ( implicit plane, line segment );
• PLANE_IMP_POINT_DIST_3D: distance ( point, implicit plane ) in 3D.
• PLANE_IMP_POINT_DIST_SIGNED_3D: signed distance ( implicit plane, point) in 3D.
• PLANE_IMP_TRIANGLE_INT_3D intersection ( implicit plane, triangle ) in 3D.
• PLANE_IMP_TRIANGLE_INT_ADD_3D is a utility for PLANE_IMP_TRIANGLE_INT_3D.
• PLANE_IMP2NORM_3D converts an implicit plane to normal form in 3D.
• PLANE_NORM_BASIS_3D finds two perpendicular vectors in a plane in 3D.
• PLANE_NORM2IMP_3D converts a normal form plane to implicit form in 3D.
• POINTS_COLIN_2D estimates the colinearity of 3 points in 2D.
• POINTS_COLIN_3D estimates the colinearity of 3 points in 3D.
• POLYGON_1_2D integrates the function 1 over a polygon in 2D.
• POLYGON_AREA_2D computes the area of a polygon in 2D.
• POLYGON_AREA_2_2D computes the area of a polygon in 2D.
• POLYGON_AREA_2_3D computes the area of a polygon in 3D.
• POLYGON_AREA_3D computes the area of a polygon in 3D.
• POLYGON_CENTROID_2D computes the centroid of a polygon in 2D.
• POLYGON_CENTROID_2_2D computes the centroid of a polygon in 2D.
• POLYGON_CENTROID_3D computes the centroid of a polygon in 3D.
• POLYGON_X_2D integrates the function X over a polygon in 2D.
• POLYGON_Y_2D integrates the function Y over a polygon in 2D.
• POLYGON_XX_2D integrates the function X*X over a polygon in 2D.
• POLYGON_XY_2D integrates the function X*Y over a polygon in 2D.
• POLYGON_YY_2D integrates the function Y*Y over a polygon in 2D.
• RMAT2_DET computes the determinant of a 2 by 2 matrix.
• RMAT2_INVERSE computes the inverse of a 2 by 2 matrix.
• RMAT3_DET computes the determinant of a 3 by 3 matrix.
• RMAT3_INVERSE computes the inverse of a 3 by 3 matrix.
• RMAT4_DET computes the determinant of a 4 by 4 matrix.
• RMAT5_DET computes the determinant of a 5 by 5 matrix.
• SPHERE_IMP_VOLUME_3D computes the volume of an implicit sphere in 3D.
• TAND returns the tangent of an angle given in degrees.
• TETRA_CENTROID_3D computes the centroid of a tetrahedron in 3D.
• TMAT_INIT initializes the geometric transformation matrix.
• TMAT_MXM multiplies two geometric transformation matrices.
• TMAT_MXP multiplies a geometric transformation matrix times a point.
• TMAT_MXP2 multiplies a geometric transformation matrix times N points.
• TMAT_MXV multiplies a geometric transformation matrix times a vector.
• TMAT_ROT_AXIS applies an axis rotation to the geometric transformation matrix.
• TMAT_ROT_VECTOR applies a rotation about a vector to the geometric transformation matrix.
• TMAT_SCALE applies a scaling to the geometric transformation matrix.
• TMAT_SHEAR applies a shear to the geometric transformation matrix.
• TMAT_TRANS applies a translation to the geometric transformation matrix.
• TORUS_VOLUME_3D computes the volume of a torus in 3D.
• TRIANGLE_AREA_2D computes the area of a triangle in 2D.
• TRIANGLE_AREA_SIGNED_2D computes the signed area of a triangle in 2D.
• TRIANGLE_AREA_3D computes the area of a triangle in 3D.
• TRIANGLE_CENTROID_2D computes the centroid of a triangle in 2D.
• TRIANGLE_CENTROID_3D computes the centroid of a triangle in 3D.
• TRIANGLE_INCIRCLE_2D computes the inscribed circle of a triangle in 2D.
• UNIFORM_01_SAMPLE computes a random value between 0 and 1.
• VECTOR_ROTATE_2D rotates a vector around the origin in 2D.
• VECTOR_ROTATE_3D rotates a vector around an axis vector in 3D.
• VECTOR_UNIT_2D normalizes a vector in 3D.
• VECTOR_UNIT_3D normalizes a vector in 3D.
• VECTOR_UNIT_ND normalizes a vector in 3D.

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