CFD Utilities Files

The geomlib collection contains single-function utilities arising from
geometric or graphical applications in 2- or 3-space.  See also the
gridlib and numodules collections for related utilities such as for
curvature calculations.

Note that the NEAREST_*_POINT utilities all return the point inside or on
the boundary of the specified cell along with interpolation coefficients
for that point, to be applied to data at the cell vertices.  The associated
squared distance may or may not be zero, because the returned point is not
allowed to be outside the cell being investigated.  This functionality is
key to the effectiveness of the ADT search packages for various mesh types
(see /adt).

Conversely, PROJECT3 and PROJECT4 allow interpolation coefficients to be
outside [0, 1], meaning the foot of the computed perpendicular may be
outside the indicated triangle or quadrilateral in 3-space.  But searching
cells until one is found for which all coefficients are within [0, 1] is
NOT the recommended strategy. The NEAREST_*_POINT utilities employed by the
ADT (Alternating Digital Tree) packages are likely to be preferable, as the
searches are not affected by whether the target point is inside the grid
being searched or outside it.  Two-space variants, nearest_edge_pt_2d and
nearest_tri_pt_2d, have most recently been prompted by the need to work with
Delaunay triangulations of (x,y) data.

Two recent additions, DETECT_VERTICES and VERTEX_CURVATURE, are now options
in CURVDIS[2] (see gridlib) as needed by the CAPSULE_GRID application.

Two more recent additions are also used by gridlib/curvdis.f: detect_flatness
and handle_flatness, for broadening high-curvature regions onto flat regions.

There are multiple ways of calculating the volume of a tetrahedron, pyramid,
and hexahedron, and their results differ slightly.  Those based on the tet
method found in Wolfram, V = | a . ( b x c) | / 6, and implemented in tet_vol
here, are the most efficient.

angle2d.f90          ! 2-space angle at point i between adjacent segments
angle_between_planes ! Angle between planes defined by two triangles
angle_between_vectors! Angle between two vectors in 3-space
arcs2d.f             ! Normalized arcs for a surface grid stored as triples
arcs3d.f             ! Normalized arcs for a volume  grid stored as triples
arcs_block_3d.f90    ! Arc lengths along any line of a 3D volume grid block
area3.f              ! 3-space triangle area; cross-products/determinants
area4.f              ! 3-space quadrilateral area, as that of 2 triangles
areaxy.f             ! 2-space polygon area; no square roots
beval.f              ! "Sine-bump" type shape functions (see PROFILE app.)
catenary_parameters.f90   ! Find a in y = a cosh (x/a) - a for given defln.
chord3d.f            ! Chord length sum between points on a 3-space curve
chord.f              ! Chord length sum between points on a 2-space curve
chords2d.f           ! Cumulative chords lengths, 2-space, normalize option
chords3d.f           ! Cumulative chords lengths, 3-space, normalize option
chordsrf.f           ! Variant of CHORDS3D for a row of a surface grid
chordsrow.f          ! 2-space analogue of CHORDSRF; normalize option
circle_slope.f90     ! Find the point on a circle with a specified slope
cross.f              ! Cross product vector of two 3-space vectors
cross_product.f90    ! Updated variant of the cross product
curv2d.f             ! Signed curvature(s) for a 2-space curve
curv3d.f             ! Arc-length-based curvature(s) for a 3-space curve
curve_diffs          ! Shortest distances between two 2-space curves
detect_flatness.f90  ! Detect low/zero-curvature regions in a distribtion
detect_vertices.f90  ! Detect 1-point spikes in a curvature distribution
distptol.f           ! Perpendicular dist. from a point to an n-space line
distptop.f           ! (Careful) distance between two points in 3-space
distptos.f           ! Distance from a 3-sp. point to a finite line segment
gaussian_curvature.f90    ! Gaussian & mean curvatures, structured surface
handle_flatness.f90       ! Companion to detect_flatness & gridlib/curvdis.f
hex_vol.f90               ! Hexahedron volume as 6 tetraheadra (recommended)
hex_volume.f90            ! Hexahedron volume as 3 quad-based pyramids
nearest_brick_point.f90   ! Structured-vol.-grid var. of nearest_hex_point
nearest_cell_point.f90    ! Nearest pt. in or on a cell of given mixed type
nearest_curve_point.f90   ! Nearest pt. not off a finite 3-space curve
nearest_edge_pt_2d.f90    ! 2-space variant of nearest_edge_point
nearest_edge_point.f90    ! Nearest pt. not off a 3-spc. 2-pt. line segment
nearest_hex_point.f90     ! Nearest pt. in or on a hex cell, Fluent order
nearest_prism_point.f90   ! To be completed if it's ever needed
nearest_pyramid_point.f90 ! To be completed if it's ever needed
nearest_quad_point.f90    ! Nearest pt. in or on a quad cell, Fluent order
nearest_tet_point.f90     ! Nearest pt. not outside a tet cell
nearest_tri_pt_2d.f90     ! 2-space variant of nearest_tri_point
nearest_tri_point.f90     ! Nearest pt. in or on a triangular cell, 3-space
param2d.f            ! [Un]normalized arc lengths in a 3-space surface grid
param2do.f           ! Variant of PARAM2D with optional Umax, Vmax outputs
paramxy.f            ! Normalized arc lengths in a 2-space structured grid
paramxyz.f           ! 3-space variant of PARAMXY (surface or volume grid)
polygon3.f           ! Centroid and area of a 2-space triangle
polygon4.f           ! Centroid and area of a 2-space quadrilateral
project3.f           ! Nearest point on a plane defined by a 3-sp. triangle
project4.f           ! Nearest point on a surface defined by a 3-sp. quad.
pyramid_volume.f90   ! Volume of a quad-based pyramid as base area*height/3
quad_area.f90        ! Quad. cell area via two cross products
rigid_transform.f90  ! Transforms interior points given new curve end pts.
rotate2.f            ! Rotate 2-space point(s) about a 2-sp. pt.
rotate2d.f           ! Rotate 2-space point(s) about a 2-sp. pt. in place
rotate3d.f           ! Rotate 3-space point(s) about a 3-sp. pt. in place
rotate_xyz.f90       ! Variant of ROTATE3D for xyz(1:3) triple(s)
solid_angle_quad.f90 ! Solid angle element at a point for quad. cell (i,j)
solid_angle_quadrature_4  ! Integn. w.r.t. solid angle at P over a quad. patch 
surface_normal.f90   ! (Careful) unit normal to a structured surface
tet_vol.f90          ! Tetrahedron volume as | a . (b x c) | / 6 (Wolfram).
tri_normal_and_area.f90   ! Unit normal, area of surface triangulation cell
unitnorm.f           ! Unit normals at points defining a 2-space curve
unitnorm2d.f90       ! Unit normal to a 2-space curve at any arc length
vertex_curvature.f90 ! Moderate 1-pt. curvature spikes at indicated indices
xderivs.f            ! Given dx/dt, dy/dt, d2*/dt2, compute dy/dx & d2y/dx2