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authorTavian Barnes <tavianator@tavianator.com>2014-08-19 17:10:03 -0400
committerTavian Barnes <tavianator@tavianator.com>2015-10-25 11:03:56 -0400
commit7b09710392d35fb55b52031d447a542d99fc6b4b (patch)
tree270eb927ee8c52ceeb99926ebf4843704775a610 /libdimension/dimension/geometry.h
parent200c86b91ea7063d35be3bffc11c5da53c054653 (diff)
downloaddimension-7b09710392d35fb55b52031d447a542d99fc6b4b.tar.xz
Modularize the libdimension codebase.
Diffstat (limited to 'libdimension/dimension/geometry.h')
-rw-r--r--libdimension/dimension/geometry.h500
1 files changed, 0 insertions, 500 deletions
diff --git a/libdimension/dimension/geometry.h b/libdimension/dimension/geometry.h
deleted file mode 100644
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--- a/libdimension/dimension/geometry.h
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-/*************************************************************************
- * Copyright (C) 2009-2014 Tavian Barnes <tavianator@tavianator.com> *
- * *
- * This file is part of The Dimension Library. *
- * *
- * The Dimension Library is free software; you can redistribute it and/ *
- * or modify it under the terms of the GNU Lesser General Public License *
- * as published by the Free Software Foundation; either version 3 of the *
- * License, or (at your option) any later version. *
- * *
- * The Dimension Library is distributed in the hope that it will be *
- * useful, but WITHOUT ANY WARRANTY; without even the implied warranty *
- * of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
- * Lesser General Public License for more details. *
- * *
- * You should have received a copy of the GNU Lesser General Public *
- * License along with this program. If not, see *
- * <http://www.gnu.org/licenses/>. *
- *************************************************************************/
-
-/**
- * @file
- * Core geometric types like vectors, matricies, and rays.
- */
-
-#include <math.h>
-#include <stdbool.h>
-
-/** A vector in 3 dimensions. */
-typedef struct dmnsn_vector {
- double x; /**< The x component. */
- double y; /**< The y component. */
- double z; /**< The z component. */
-} dmnsn_vector;
-
-/** A standard format string for vectors. */
-#define DMNSN_VECTOR_FORMAT "<%g, %g, %g>"
-/** The appropriate arguements to printf() a vector. */
-#define DMNSN_VECTOR_PRINTF(v) (v).x, (v).y, (v).z
-
-/** A 4x4 affine transformation matrix, with implied [0 0 0 1] bottom row. */
-typedef struct dmnsn_matrix {
- double n[3][4]; /**< The matrix elements in row-major order. */
-} dmnsn_matrix;
-
-/** A standard format string for matricies. */
-#define DMNSN_MATRIX_FORMAT \
- "[%g\t%g\t%g\t%g]\n" \
- "[%g\t%g\t%g\t%g]\n" \
- "[%g\t%g\t%g\t%g]\n" \
- "[%g\t%g\t%g\t%g]"
-/** The appropriate arguements to printf() a matrix. */
-#define DMNSN_MATRIX_PRINTF(m) \
- (m).n[0][0], (m).n[0][1], (m).n[0][2], (m).n[0][3], \
- (m).n[1][0], (m).n[1][1], (m).n[1][2], (m).n[1][3], \
- (m).n[2][0], (m).n[2][1], (m).n[2][2], (m).n[2][3], \
- 0.0, 0.0, 0.0, 1.0
-
-/** A line, or ray. */
-typedef struct dmnsn_line {
- dmnsn_vector x0; /**< A point on the line. */
- dmnsn_vector n; /**< A normal vector; the direction of the line. */
-} dmnsn_line;
-
-/** A standard format string for lines. */
-#define DMNSN_LINE_FORMAT "(<%g, %g, %g> + t*<%g, %g, %g>)"
-/** The appropriate arguements to printf() a line. */
-#define DMNSN_LINE_PRINTF(l) \
- DMNSN_VECTOR_PRINTF((l).x0), DMNSN_VECTOR_PRINTF((l).n)
-
-/** An axis-aligned bounding box (AABB). */
-typedef struct dmnsn_bounding_box {
- dmnsn_vector min; /**< The coordinate-wise minimum extent of the box. */
- dmnsn_vector max; /**< The coordinate-wise maximum extent of the box. */
-} dmnsn_bounding_box;
-
-/** A standard format string for bounding boxes. */
-#define DMNSN_BOUNDING_BOX_FORMAT "(<%g, %g, %g> ==> <%g, %g, %g>)"
-/** The appropriate arguements to printf() a bounding box. */
-#define DMNSN_BOUNDING_BOX_PRINTF(box) \
- DMNSN_VECTOR_PRINTF((box).min), DMNSN_VECTOR_PRINTF((box).max)
-
-/* Constants */
-
-/** The zero vector. */
-static const dmnsn_vector dmnsn_zero = { 0.0, 0.0, 0.0 };
-/** The x vector. */
-static const dmnsn_vector dmnsn_x = { 1.0, 0.0, 0.0 };
-/** The y vector. */
-static const dmnsn_vector dmnsn_y = { 0.0, 1.0, 0.0 };
-/** The z vector. */
-static const dmnsn_vector dmnsn_z = { 0.0, 0.0, 1.0 };
-
-/* Shorthand for vector/matrix construction */
-
-/** Construct a new vector. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_new_vector(double x, double y, double z)
-{
- dmnsn_vector v = { x, y, z };
- return v;
-}
-
-/** Construct a new transformation matrix. */
-DMNSN_INLINE dmnsn_matrix
-dmnsn_new_matrix(double a0, double a1, double a2, double a3,
- double b0, double b1, double b2, double b3,
- double c0, double c1, double c2, double c3)
-{
- dmnsn_matrix m = { { { a0, a1, a2, a3 },
- { b0, b1, b2, b3 },
- { c0, c1, c2, c3 } } };
- return m;
-}
-
-/** Construct a new transformation matrix from column vectors. */
-DMNSN_INLINE dmnsn_matrix
-dmnsn_new_matrix4(dmnsn_vector a, dmnsn_vector b, dmnsn_vector c,
- dmnsn_vector d)
-{
- dmnsn_matrix m = { { { a.x, b.x, c.x, d.x },
- { a.y, b.y, c.y, d.y },
- { a.z, b.z, c.z, d.z } } };
- return m;
-}
-
-/** Extract column vectors from a matrix. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_matrix_column(dmnsn_matrix M, unsigned int i)
-{
- return dmnsn_new_vector(M.n[0][i], M.n[1][i], M.n[2][i]);
-}
-
-/** Return the identity matrix. */
-dmnsn_matrix dmnsn_identity_matrix(void);
-
-/**
- * A scale transformation.
- * @param[in] s A vector with components representing the scaling factor in
- * each axis.
- * @return The transformation matrix.
- */
-dmnsn_matrix dmnsn_scale_matrix(dmnsn_vector s);
-/**
- * A translation.
- * @param[in] d The vector to translate by.
- * @return The transformation matrix.
- */
-dmnsn_matrix dmnsn_translation_matrix(dmnsn_vector d);
-/**
- * A left-handed rotation.
- * @param[in] theta A vector representing an axis and angle.
- * @f$ axis = \vec{\theta}/|\vec{\theta}| @f$,
- * @f$ angle = |\vec{\theta}| @f$
- * @return The transformation matrix.
- */
-dmnsn_matrix dmnsn_rotation_matrix(dmnsn_vector theta);
-/**
- * An alignment matrix.
- * @param[in] from The initial vector.
- * @param[in] to The desired direction.
- * @param[in] axis1 The first axis about which to rotate.
- * @param[in] axis2 The second axis about which to rotate.
- * @return A transformation matrix that will rotate \p from to \p to.
- */
-dmnsn_matrix dmnsn_alignment_matrix(dmnsn_vector from, dmnsn_vector to,
- dmnsn_vector axis1, dmnsn_vector axis2);
-
-/**
- * Construct a new line.
- * @param[in] x0 A point on the line.
- * @param[in] n The direction of the line.
- * @return The new line.
- */
-DMNSN_INLINE dmnsn_line
-dmnsn_new_line(dmnsn_vector x0, dmnsn_vector n)
-{
- dmnsn_line l = { x0, n };
- return l;
-}
-
-/**
- * Construct a new bounding box.
- * @param[in] min The minimal extent of the bounding box.
- * @param[in] max The maximal extent of the bounding box.
- * @return The new bounding box.
- */
-DMNSN_INLINE dmnsn_bounding_box
-dmnsn_new_bounding_box(dmnsn_vector min, dmnsn_vector max)
-{
- dmnsn_bounding_box box = { min, max };
- return box;
-}
-
-/** Return the bounding box which contains nothing. */
-DMNSN_INLINE dmnsn_bounding_box
-dmnsn_zero_bounding_box(void)
-{
- dmnsn_bounding_box box = {
- { DMNSN_INFINITY, DMNSN_INFINITY, DMNSN_INFINITY },
- { -DMNSN_INFINITY, -DMNSN_INFINITY, -DMNSN_INFINITY }
- };
- return box;
-}
-
-/** Return the bounding box which contains everything. */
-DMNSN_INLINE dmnsn_bounding_box
-dmnsn_infinite_bounding_box(void)
-{
- dmnsn_bounding_box box = {
- { -DMNSN_INFINITY, -DMNSN_INFINITY, -DMNSN_INFINITY },
- { DMNSN_INFINITY, DMNSN_INFINITY, DMNSN_INFINITY }
- };
- return box;
-}
-
-/* Vector and matrix arithmetic */
-
-/** Negate a vector. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_negate(dmnsn_vector rhs)
-{
- /* 3 negations */
- dmnsn_vector v = { -rhs.x, -rhs.y, -rhs.z };
- return v;
-}
-
-/** Add two vectors. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_add(dmnsn_vector lhs, dmnsn_vector rhs)
-{
- /* 3 additions */
- dmnsn_vector v = { lhs.x + rhs.x, lhs.y + rhs.y, lhs.z + rhs.z };
- return v;
-}
-
-/** Subtract two vectors. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_sub(dmnsn_vector lhs, dmnsn_vector rhs)
-{
- /* 3 additions */
- dmnsn_vector v = { lhs.x - rhs.x, lhs.y - rhs.y, lhs.z - rhs.z };
- return v;
-}
-
-/** Multiply a vector by a scalar. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_mul(double lhs, dmnsn_vector rhs)
-{
- /* 3 multiplications */
- dmnsn_vector v = { lhs*rhs.x, lhs*rhs.y, lhs*rhs.z };
- return v;
-}
-
-/** Divide a vector by a scalar. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_div(dmnsn_vector lhs, double rhs)
-{
- /* 3 divisions */
- dmnsn_vector v = { lhs.x/rhs, lhs.y/rhs, lhs.z/rhs };
- return v;
-}
-
-/** Return the dot product of two vectors. */
-DMNSN_INLINE double
-dmnsn_vector_dot(dmnsn_vector lhs, dmnsn_vector rhs)
-{
- /* 3 multiplications, 2 additions */
- return lhs.x*rhs.x + lhs.y*rhs.y + lhs.z*rhs.z;
-}
-
-/** Return the cross product of two vectors. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_cross(dmnsn_vector lhs, dmnsn_vector rhs)
-{
- /* 6 multiplications, 3 additions */
- dmnsn_vector v = { lhs.y*rhs.z - lhs.z*rhs.y,
- lhs.z*rhs.x - lhs.x*rhs.z,
- lhs.x*rhs.y - lhs.y*rhs.x };
- return v;
-}
-
-/** Return the projection of \p u onto \p d. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_proj(dmnsn_vector u, dmnsn_vector d)
-{
- /* 1 division, 9 multiplications, 4 additions */
- return dmnsn_vector_mul(dmnsn_vector_dot(u, d)/dmnsn_vector_dot(d, d), d);
-}
-
-/** Return the magnitude of a vector. */
-DMNSN_INLINE double
-dmnsn_vector_norm(dmnsn_vector n)
-{
- /* 1 sqrt, 3 multiplications, 2 additions */
- return sqrt(dmnsn_vector_dot(n, n));
-}
-
-/** Return the direction of a vector. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_normalized(dmnsn_vector n)
-{
- /* 1 sqrt, 3 divisions, 3 multiplications, 2 additions */
- return dmnsn_vector_div(n, dmnsn_vector_norm(n));
-}
-
-/** Return the component-wise minimum of two vectors. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_min(dmnsn_vector a, dmnsn_vector b)
-{
- return dmnsn_new_vector(
- dmnsn_min(a.x, b.x),
- dmnsn_min(a.y, b.y),
- dmnsn_min(a.z, b.z)
- );
-}
-
-/** Return the component-wise maximum of two vectors. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_vector_max(dmnsn_vector a, dmnsn_vector b)
-{
- return dmnsn_new_vector(
- dmnsn_max(a.x, b.x),
- dmnsn_max(a.y, b.y),
- dmnsn_max(a.z, b.z)
- );
-}
-
-/** Invert a matrix. */
-dmnsn_matrix dmnsn_matrix_inverse(dmnsn_matrix A);
-
-/** Multiply two matricies. */
-dmnsn_matrix dmnsn_matrix_mul(dmnsn_matrix lhs, dmnsn_matrix rhs);
-
-/** Transform a point by a matrix. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_transform_point(dmnsn_matrix T, dmnsn_vector v)
-{
- /* 9 multiplications, 9 additions */
- dmnsn_vector r;
- r.x = T.n[0][0]*v.x + T.n[0][1]*v.y + T.n[0][2]*v.z + T.n[0][3];
- r.y = T.n[1][0]*v.x + T.n[1][1]*v.y + T.n[1][2]*v.z + T.n[1][3];
- r.z = T.n[2][0]*v.x + T.n[2][1]*v.y + T.n[2][2]*v.z + T.n[2][3];
- return r;
-}
-
-/** Transform a direction by a matrix. */
-DMNSN_INLINE dmnsn_vector
-dmnsn_transform_direction(dmnsn_matrix T, dmnsn_vector v)
-{
- /* 9 multiplications, 6 additions */
- dmnsn_vector r;
- r.x = T.n[0][0]*v.x + T.n[0][1]*v.y + T.n[0][2]*v.z;
- r.y = T.n[1][0]*v.x + T.n[1][1]*v.y + T.n[1][2]*v.z;
- r.z = T.n[2][0]*v.x + T.n[2][1]*v.y + T.n[2][2]*v.z;
- return r;
-}
-
-/**
- * Transform a pseudovector by a matrix.
- * @param[in] Tinv The inverse of the transformation matrix.
- * @param[in] v The pseudovector to transform
- * @return The transformed pseudovector.
- */
-DMNSN_INLINE dmnsn_vector
-dmnsn_transform_normal(dmnsn_matrix Tinv, dmnsn_vector v)
-{
- /* Multiply by the transpose of the inverse
- (9 multiplications, 6 additions) */
- dmnsn_vector r;
- r.x = Tinv.n[0][0]*v.x + Tinv.n[1][0]*v.y + Tinv.n[2][0]*v.z;
- r.y = Tinv.n[0][1]*v.x + Tinv.n[1][1]*v.y + Tinv.n[2][1]*v.z;
- r.z = Tinv.n[0][2]*v.x + Tinv.n[1][2]*v.y + Tinv.n[2][2]*v.z;
- return r;
-}
-
-/** Transform a bounding box by a matrix. */
-dmnsn_bounding_box dmnsn_transform_bounding_box(dmnsn_matrix T,
- dmnsn_bounding_box box);
-
-/**
- * Transform a line by a matrix.
- * \f$ n' = T(l.\vec{x_0} + l.\vec{n}) - T(l.\vec{x_0}) \f$,
- * \f$ \vec{x_0}' = T(l.\vec{x_0}) \f$
- */
-DMNSN_INLINE dmnsn_line
-dmnsn_transform_line(dmnsn_matrix T, dmnsn_line l)
-{
- /* 18 multiplications, 15 additions */
- dmnsn_line ret;
- ret.x0 = dmnsn_transform_point(T, l.x0);
- ret.n = dmnsn_transform_direction(T, l.n);
- return ret;
-}
-
-/**
- * Return the point at \p t on a line.
- * The point is defined by \f$ l.\vec{x_0} + t \cdot l.\vec{n} \f$
- */
-DMNSN_INLINE dmnsn_vector
-dmnsn_line_point(dmnsn_line l, double t)
-{
- return dmnsn_vector_add(l.x0, dmnsn_vector_mul(t, l.n));
-}
-
-/** Add epsilon*l.n to l.x0, to avoid self-intersections. */
-DMNSN_INLINE dmnsn_line
-dmnsn_line_add_epsilon(dmnsn_line l)
-{
- return dmnsn_new_line(
- dmnsn_vector_add(
- l.x0,
- dmnsn_vector_mul(1.0e3*dmnsn_epsilon, l.n)
- ),
- l.n
- );
-}
-
-/**
- * Construct a new symmetric bounding box.
- * @param[in] r The extent of the bounding box from the origin.
- * @return The new bounding box.
- */
-DMNSN_INLINE dmnsn_bounding_box
-dmnsn_symmetric_bounding_box(dmnsn_vector r)
-{
- dmnsn_vector minus_r = dmnsn_vector_negate(r);
- dmnsn_bounding_box box = {
- dmnsn_vector_min(r, minus_r),
- dmnsn_vector_max(r, minus_r)
- };
- return box;
-}
-
-/** Return whether \p p is within the axis-aligned bounding box. */
-DMNSN_INLINE bool
-dmnsn_bounding_box_contains(dmnsn_bounding_box box, dmnsn_vector p)
-{
- return (p.x >= box.min.x && p.y >= box.min.y && p.z >= box.min.z)
- && (p.x <= box.max.x && p.y <= box.max.y && p.z <= box.max.z);
-}
-
-/** Return whether a bounding box is infinite. */
-DMNSN_INLINE bool
-dmnsn_bounding_box_is_infinite(dmnsn_bounding_box box)
-{
- return box.min.x == -DMNSN_INFINITY;
-}
-
-/**
- * Expand a bounding box to contain a point
- * @param[in] box The bounding box to expand.
- * @param[in] point The point to swallow.
- * @return The expanded bounding box.
- */
-DMNSN_INLINE dmnsn_bounding_box
-dmnsn_bounding_box_swallow(dmnsn_bounding_box box, dmnsn_vector point)
-{
- dmnsn_bounding_box ret = {
- dmnsn_vector_min(box.min, point),
- dmnsn_vector_max(box.max, point)
- };
- return ret;
-}
-
-/** Return whether a vector contains any NaN components. */
-DMNSN_INLINE bool
-dmnsn_vector_isnan(dmnsn_vector v)
-{
- return dmnsn_isnan(v.x) || dmnsn_isnan(v.y) || dmnsn_isnan(v.z);
-}
-
-/** Return whether a matrix contains any NaN components. */
-DMNSN_INLINE bool
-dmnsn_matrix_isnan(dmnsn_matrix m)
-{
- size_t i, j;
- for (i = 0; i < 3; ++i) {
- for (j = 0; j < 4; ++j) {
- if (dmnsn_isnan(m.n[i][j])) {
- return true;
- }
- }
- }
- return false;
-}
-
-/** Return whether a line contains any NaN entries. */
-DMNSN_INLINE bool
-dmnsn_line_isnan(dmnsn_line l)
-{
- return dmnsn_vector_isnan(l.x0) || dmnsn_vector_isnan(l.n);
-}
-
-/** Return whether a bounding box has any NaN components. */
-DMNSN_INLINE bool
-dmnsn_bounding_box_isnan(dmnsn_bounding_box box)
-{
- return dmnsn_vector_isnan(box.min) || dmnsn_vector_isnan(box.max);
-}