diff options
Diffstat (limited to 'libdimension/dimension/geometry.h')
| -rw-r--r-- | libdimension/dimension/geometry.h | 159 |
1 files changed, 79 insertions, 80 deletions
diff --git a/libdimension/dimension/geometry.h b/libdimension/dimension/geometry.h index b2ba551..fd4a781 100644 --- a/libdimension/dimension/geometry.h +++ b/libdimension/dimension/geometry.h @@ -26,105 +26,105 @@ #include <math.h> #include <stdbool.h> -/** A vector in 3 dimensions. */ +/// A vector in 3 dimensions. typedef struct dmnsn_vector { - double x; /**< The x component. */ - double y; /**< The y component. */ - double z; /**< The z component. */ + double x; ///< The x component. + double y; ///< The y component. + double z; ///< The z component. } dmnsn_vector; -/** A standard format string for vectors. */ +/// A standard format string for vectors. #define DMNSN_VECTOR_FORMAT "<%g, %g, %g>" -/** The appropriate arguements to printf() a vector. */ +/// 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. */ +/// 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. */ + double n[3][4]; ///< The matrix elements in row-major order. } dmnsn_matrix; -/** A standard format string for matricies. */ +/// 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. */ +/// 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. */ +/// 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_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. */ +/// A standard format string for lines. #define DMNSN_LINE_FORMAT "(<%g, %g, %g> + t*<%g, %g, %g>)" -/** The appropriate arguements to printf() a line. */ +/// 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). */ +/// 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_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. */ +/// 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. */ +/// 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 */ +// Constants -/** The smallest value considered non-zero by some numerical algorithms. */ +/// The smallest value considered non-zero by some numerical algorithms. #define dmnsn_epsilon 1.0e-10 -/** The zero vector. */ +/// The zero vector. static const dmnsn_vector dmnsn_zero = { 0.0, 0.0, 0.0 }; -/** The x vector. */ +/// The x vector. static const dmnsn_vector dmnsn_x = { 1.0, 0.0, 0.0 }; -/** The y vector. */ +/// The y vector. static const dmnsn_vector dmnsn_y = { 0.0, 1.0, 0.0 }; -/** The z vector. */ +/// The z vector. static const dmnsn_vector dmnsn_z = { 0.0, 0.0, 1.0 }; -/* Scalar functions */ +// Scalar functions -/** Find the minimum of two scalars. */ +/// Find the minimum of two scalars. DMNSN_INLINE double dmnsn_min(double a, double b) { return a < b ? a : b; } -/** Find the maximum of two scalars. */ +/// Find the maximum of two scalars. DMNSN_INLINE double dmnsn_max(double a, double b) { return a > b ? a : b; } -/** Convert degrees to radians. */ +/// Convert degrees to radians. DMNSN_INLINE double dmnsn_radians(double degrees) { return degrees*atan(1.0)/45.0; } -/** Convert radians to degrees. */ +/// Convert radians to degrees. DMNSN_INLINE double dmnsn_degrees(double radians) { return radians*45.0/atan(1.0); } -/** Return the sign of a scalar. */ +/// Return the sign of a scalar. DMNSN_INLINE int dmnsn_sign(double n) { @@ -137,9 +137,9 @@ dmnsn_sign(double n) } } -/* Shorthand for vector/matrix construction */ +// Shorthand for vector/matrix construction -/** Construct a new vector. */ +/// Construct a new vector. DMNSN_INLINE dmnsn_vector dmnsn_new_vector(double x, double y, double z) { @@ -147,7 +147,7 @@ dmnsn_new_vector(double x, double y, double z) return v; } -/** Construct a new transformation matrix. */ +/// 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, @@ -159,7 +159,7 @@ dmnsn_new_matrix(double a0, double a1, double a2, double a3, return m; } -/** Construct a new transformation matrix from column vectors. */ +/// 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) @@ -170,14 +170,14 @@ dmnsn_new_matrix4(dmnsn_vector a, dmnsn_vector b, dmnsn_vector c, return m; } -/** Extract column vectors from a matrix. */ +/// 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. */ +/// Return the identity matrix. dmnsn_matrix dmnsn_identity_matrix(void); /** @@ -238,7 +238,7 @@ dmnsn_new_bounding_box(dmnsn_vector min, dmnsn_vector max) return box; } -/** Return the bounding box which contains nothing. */ +/// Return the bounding box which contains nothing. DMNSN_INLINE dmnsn_bounding_box dmnsn_zero_bounding_box(void) { @@ -249,7 +249,7 @@ dmnsn_zero_bounding_box(void) return box; } -/** Return the bounding box which contains everything. */ +/// Return the bounding box which contains everything. DMNSN_INLINE dmnsn_bounding_box dmnsn_infinite_bounding_box(void) { @@ -260,97 +260,97 @@ dmnsn_infinite_bounding_box(void) return box; } -/* Vector and matrix arithmetic */ +// Vector and matrix arithmetic -/** Negate a vector. */ +/// Negate a vector. DMNSN_INLINE dmnsn_vector dmnsn_vector_negate(dmnsn_vector rhs) { - /* 3 negations */ + // 3 negations dmnsn_vector v = { -rhs.x, -rhs.y, -rhs.z }; return v; } -/** Add two vectors. */ +/// Add two vectors. DMNSN_INLINE dmnsn_vector dmnsn_vector_add(dmnsn_vector lhs, dmnsn_vector rhs) { - /* 3 additions */ + // 3 additions dmnsn_vector v = { lhs.x + rhs.x, lhs.y + rhs.y, lhs.z + rhs.z }; return v; } -/** Subtract two vectors. */ +/// Subtract two vectors. DMNSN_INLINE dmnsn_vector dmnsn_vector_sub(dmnsn_vector lhs, dmnsn_vector rhs) { - /* 3 additions */ + // 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. */ +/// Multiply a vector by a scalar. DMNSN_INLINE dmnsn_vector dmnsn_vector_mul(double lhs, dmnsn_vector rhs) { - /* 3 multiplications */ + // 3 multiplications dmnsn_vector v = { lhs*rhs.x, lhs*rhs.y, lhs*rhs.z }; return v; } -/** Divide a vector by a scalar. */ +/// Divide a vector by a scalar. DMNSN_INLINE dmnsn_vector dmnsn_vector_div(dmnsn_vector lhs, double rhs) { - /* 3 divisions */ + // 3 divisions dmnsn_vector v = { lhs.x/rhs, lhs.y/rhs, lhs.z/rhs }; return v; } -/** Return the dot product of two vectors. */ +/// Return the dot product of two vectors. DMNSN_INLINE double dmnsn_vector_dot(dmnsn_vector lhs, dmnsn_vector rhs) { - /* 3 multiplications, 2 additions */ + // 3 multiplications, 2 additions return lhs.x*rhs.x + lhs.y*rhs.y + lhs.z*rhs.z; } -/** Return the cross product of two vectors. */ +/// Return the cross product of two vectors. DMNSN_INLINE dmnsn_vector dmnsn_vector_cross(dmnsn_vector lhs, dmnsn_vector rhs) { - /* 6 multiplications, 3 additions */ + // 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. */ +/// 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 */ + // 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. */ +/// Return the magnitude of a vector. DMNSN_INLINE double dmnsn_vector_norm(dmnsn_vector n) { - /* 1 sqrt, 3 multiplications, 2 additions */ + // 1 sqrt, 3 multiplications, 2 additions return sqrt(dmnsn_vector_dot(n, n)); } -/** Return the direction of a vector. */ +/// Return the direction of a vector. DMNSN_INLINE dmnsn_vector dmnsn_vector_normalized(dmnsn_vector n) { - /* 1 sqrt, 3 divisions, 3 multiplications, 2 additions */ + // 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. */ +/// Return the component-wise minimum of two vectors. DMNSN_INLINE dmnsn_vector dmnsn_vector_min(dmnsn_vector a, dmnsn_vector b) { @@ -361,7 +361,7 @@ dmnsn_vector_min(dmnsn_vector a, dmnsn_vector b) ); } -/** Return the component-wise maximum of two vectors. */ +/// Return the component-wise maximum of two vectors. DMNSN_INLINE dmnsn_vector dmnsn_vector_max(dmnsn_vector a, dmnsn_vector b) { @@ -372,17 +372,17 @@ dmnsn_vector_max(dmnsn_vector a, dmnsn_vector b) ); } -/** Invert a matrix. */ +/// Invert a matrix. dmnsn_matrix dmnsn_matrix_inverse(dmnsn_matrix A); -/** Multiply two matricies. */ +/// Multiply two matricies. dmnsn_matrix dmnsn_matrix_mul(dmnsn_matrix lhs, dmnsn_matrix rhs); -/** Transform a point by a matrix. */ +/// Transform a point by a matrix. DMNSN_INLINE dmnsn_vector dmnsn_transform_point(dmnsn_matrix T, dmnsn_vector v) { - /* 9 multiplications, 9 additions */ + // 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]; @@ -390,11 +390,11 @@ dmnsn_transform_point(dmnsn_matrix T, dmnsn_vector v) return r; } -/** Transform a direction by a matrix. */ +/// Transform a direction by a matrix. DMNSN_INLINE dmnsn_vector dmnsn_transform_direction(dmnsn_matrix T, dmnsn_vector v) { - /* 9 multiplications, 6 additions */ + // 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; @@ -411,8 +411,7 @@ dmnsn_transform_direction(dmnsn_matrix T, dmnsn_vector v) DMNSN_INLINE dmnsn_vector dmnsn_transform_normal(dmnsn_matrix Tinv, dmnsn_vector v) { - /* Multiply by the transpose of the inverse - (9 multiplications, 6 additions) */ + // 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; @@ -420,7 +419,7 @@ dmnsn_transform_normal(dmnsn_matrix Tinv, dmnsn_vector v) return r; } -/** Transform a bounding box by a matrix. */ +/// Transform a bounding box by a matrix. dmnsn_bounding_box dmnsn_transform_bounding_box(dmnsn_matrix T, dmnsn_bounding_box box); @@ -432,7 +431,7 @@ dmnsn_bounding_box dmnsn_transform_bounding_box(dmnsn_matrix T, DMNSN_INLINE dmnsn_line dmnsn_transform_line(dmnsn_matrix T, dmnsn_line l) { - /* 18 multiplications, 24 additions */ + // 18 multiplications, 24 additions dmnsn_line ret; ret.x0 = dmnsn_transform_point(T, l.x0); ret.n = dmnsn_transform_direction(T, l.n); @@ -449,7 +448,7 @@ 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. */ +/// Add epsilon*l.n to l.x0, to avoid self-intersections. DMNSN_INLINE dmnsn_line dmnsn_line_add_epsilon(dmnsn_line l) { @@ -478,7 +477,7 @@ dmnsn_symmetric_bounding_box(dmnsn_vector r) return box; } -/** Return whether \p p is within the axis-aligned bounding 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) { @@ -486,7 +485,7 @@ dmnsn_bounding_box_contains(dmnsn_bounding_box box, dmnsn_vector p) && (p.x <= box.max.x && p.y <= box.max.y && p.z <= box.max.z); } -/** Return whether a bounding box is infinite. */ +/// Return whether a bounding box is infinite. DMNSN_INLINE bool dmnsn_bounding_box_is_infinite(dmnsn_bounding_box box) { @@ -509,14 +508,14 @@ dmnsn_bounding_box_swallow(dmnsn_bounding_box box, dmnsn_vector point) return ret; } -/** Return whether a vector contains any NaN components. */ +/// Return whether a vector contains any NaN components. DMNSN_INLINE bool dmnsn_vector_isnan(dmnsn_vector v) { return isnan(v.x) || isnan(v.y) || isnan(v.z); } -/** Return whether a matrix contains any NaN components. */ +/// Return whether a matrix contains any NaN components. DMNSN_INLINE bool dmnsn_matrix_isnan(dmnsn_matrix m) { @@ -531,14 +530,14 @@ dmnsn_matrix_isnan(dmnsn_matrix m) return false; } -/** Return whether a line contains any NaN entries. */ +/// 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. */ +/// Return whether a bounding box has any NaN components. DMNSN_INLINE bool dmnsn_bounding_box_isnan(dmnsn_bounding_box box) { |