VecForVector algebra for Fortran

One vector type, written as you write the maths: a + b, 2 * a, a .dot. b, a .cross. b. Lengths, angles, face normals, distances, projections, rotations and mirrors, in single, double or quadruple precision, on whole arrays at once, and inside an OpenACC kernel.

Tutorial

Cookbook

Reference

API

View on GitHub

➕

The maths, as you write it

a + b, a - b, -a, 2 * a, a / 4, a .dot. b, a .cross. b, a .paral. n, a .ortho. n, R .matrix. a: a scalar of any integer or real kind on either side, converted for you.

Arithmetic

📐

Lengths, angles, directions

normL2, sq_norm, a unit vector in place or as a copy, the angle between two vectors with atan2, so it is accurate near 0 and 180 degrees.

Lengths and angles

🔺

Faces of a mesh

The normal of a triangle or a quadrilateral, as long as the face is large or of unit length: areas, outward normals, the volume of a body by the divergence theorem.

Faces, area, volume

📍

Points, lines, planes

The distance from a line, the signed distance from a plane, the foot of a point on it, collinear and concyclic points, with a tolerance when the points are computed.

A point and the body

🔄

Rotations and mirrors

A rotation about any axis, a reflection across any plane, as a call or as a matrix computed once and applied to many vectors.

Rotations and mirrors

🧮

Whole arrays at once

Every operator and function is elemental: one call computes the normals of all the faces, or the distances of a million points.

Many vectors at once

🎚️

Single, double, quadruple

vector_R4P, vector_R8P, vector_R16P, each with its versors and functions, from one use vecfor; the default vector is double precision.

Precision

🚀

On the GPU

A device-callable API for OpenACC kernels: sum, difference, scaling, dot and cross products, assignment, the same results as the operators.

On the GPU

a tetrahedron with its outward unit normals, a point q outside it and its foot on the slanted face

The tetrahedron of the tutorial: its outward face normals, a point q and its foot on the slanted face. Every figure of these pages is computed by VecFor, projected onto the page with its own dot product, and drawn by foresight.

Quick start

A triangle in space, its normal and area, an angle, a point above it, its distance and its foot: this is a whole program.

f90

program quickstart
!< Quick start: a triangle in space, its normal and area, a point above it, its distance and its foot.
use penf, only : R8P
use vecfor, only : angle, ex, ey, ez, face_normal3, vector
implicit none
type(vector) :: a, b, c ! the corners of a triangle
type(vector) :: n       ! its normal
type(vector) :: q       ! a point
type(vector) :: foot    ! its projection onto the plane of the triangle

a = ex
b = ey
c = ez
n = face_normal3(pt1=a, pt2=b, pt3=c)                 ! as long as the triangle is large
call n%printf(prefix='normal   = ')
print '(A,F7.4)', 'area     = ', n%normL2()
print '(A,F7.4)', 'angle    = ', angle(b - a, c - a) * 180 / acos(-1._R8P)
q = 0.8_R8P * ex + 0.6_R8P * ey + 0.8_R8P * ez
print '(A,F7.4)', 'distance = ', q%distance_to_plane(pt1=a, pt2=b, pt3=c)
foot = q%projection_onto_plane(pt1=a, pt2=b, pt3=c)
print '(A,3F7.4)', 'foot     = ', foot%x, foot%y, foot%z
endprogram quickstart

console

$ quickstart
normal   = +0.5, +0.5, +0.5
area     =  0.8660
angle    = 60.0000
distance =  0.6928
foot     =  0.4000 0.2000 0.4000

Gallery

Each figure is the output of a program of the docs; the title leads to the recipe or the chapter that computes it.

two vectors, the parallelogram they span and their cross product — The cross product

a triangle and a quadrilateral with their normals, one as long as the face is large and one of unit length — Face normals and areas

a velocity hitting a wall, split into normal and tangential components, and the velocity after the bounce — A slip wall: .paral. and .ortho.

a point, a line through two points, the distance between them and a point on the line — The distance from a line

the unit vector along x rotated about the diagonal in twelve steps, on a cone — A rotation about an axis

a tetrahedron and its mirror image across an oblique plane — A mirror across a plane

the circle through the three corners of a triangle and a fourth point on it — Concyclic points

the points of a grid that lie inside a tetrahedron — Inside or outside, a grid at once

Where next

Learn VecFor step by step in the tutorial, find quick answers in the cookbook, look up every operator and method in the reference.

Authors

Stefano Zaghi — @szaghi

Contributions are welcome — see the Contributing page.

VecForVector algebra for Fortran

The maths, as you write it

Lengths, angles, directions

Faces of a mesh

Points, lines, planes

Rotations and mirrors

Whole arrays at once

Single, double, quadruple

On the GPU

Quick start ​

Gallery ​

Where next ​

Authors ​

Quick start

Gallery

Where next

Authors