# [−][src]Module pbrt::core::geometry

Almost all nontrivial graphics programs are built on a foundation of geometric classes. These classes represent mathematical constructs like points, vectors, and rays.

# Points

A point is a zero-dimensional location in 2D or 3D space. The Point2 and Point3 classes in pbrt represent points in the obvious way: using x, y, z (in 3D) coordinates with respect to a coordinate system. Although the same representation is used for vectors, the fact that a point represents a position whereas a vector represents a direction leads to a number of important differences in how they are treated.

```extern crate pbrt;

use pbrt::core::geometry::Point3;

fn main() {
let int_origin = Point3 { x: 0, y: 0, z: 0 };
let float_origin = Point3 {
x: 0.0,
y: 0.0,
z: 0.0,
};

println!("int   {:?}", int_origin);
println!("float {:?}", float_origin);
}```

# Vectors

pbrt provides both 2D and 3D vector classes. Both are parameterized by the type of the underlying vector element, thus making it easy to instantiate vectors of both integer and floating-point types.

```extern crate pbrt;

use pbrt::core::geometry::Vector3;

fn main() {
let int_null = Vector3 { x: 0, y: 0, z: 0 };
let float_null = Vector3 {
x: 0.0,
y: 0.0,
z: 0.0,
};

println!("int   {:?}", int_null);
println!("float {:?}", float_null);
}```

# Normals

A surface normal (or just normal) is a vector that is perpendicular to a surface at a particular position. It can be defined as the cross product of any two nonparallel vectors that are tangent to the surface at a point. Although normals are superficially similar to vectors, it is important to distinguish between the two of them: because normals are defined in terms of their relationship to a particular surface, they behave differently than vectors in some situations, particularly when applying transformations.

```extern crate pbrt;

use pbrt::core::geometry::Normal3;

fn main() {
let int_null = Normal3 { x: 0, y: 0, z: 0 };
let float_null = Normal3 {
x: 0.0,
y: 0.0,
z: 0.0,
};

println!("int   {:?}", int_null);
println!("float {:?}", float_null);
}```

# Rays

A ray is a semi-infinite line specified by its origin and direction. pbrt represents a Ray with a Point3f for the origin and a Vector3f for the direction. We only need rays with floating-point origins and directions, so Ray isn't a template class parameterized by an arbitrary type, as points, vectors, and normals were.

```extern crate pbrt;

use pbrt::core::geometry::{Ray, Point3f, Vector3f};

fn main() {
let origin = Point3f {
x: -5.5,
y: 2.75,
z: 0.0,
};
let direction = Vector3f {
x: 1.0,
y: -8.75,
z: 2.25,
};
let ray = Ray {
o: origin,
d: direction,
t_max: std::f32::INFINITY,
time: 0.0,
medium: None,
differential: None,
};
}```

## RayDifferentials

RayDifferential is a subclass of Ray that contains additional information about two auxiliary rays. These extra rays represent camera rays offset by one sample in the x and y direction from the main ray on the film plane. By determining the area that these three rays project on an object being shaded, the Texture can estimate an area to average over for proper antialiasing.

In Rust we don't have inheritance, therefore we use an Option in the Ray struct, which means the additional information can be present (or not).

# Bounding Boxes

Many parts of the system operate on axis-aligned regions of space. For example, multi-threading in pbrt is implemented by subdividing the image into rectangular tiles that can be processed independently, and the bounding volume hierarchy uses 3D boxes to bound geometric primitives in the scene. The Bounds2 and Bounds3 template classes are used to represent the extent of these sort of regions. Both are parameterized by a type T that is used to represent the coordinates of its extents.

```extern crate pbrt;

use pbrt::core::geometry::{Bounds3, Point3};

fn main() {
let int_origin = Point3 { x: 0, y: 0, z: 0 };
let int_xyz111 = Point3 { x: 1, y: 1, z: 1 };
let float_origin = Point3 {
x: 0.0,
y: 0.0,
z: 0.0,
};
let float_xyz111 = Point3 {
x: 1.0,
y: 1.0,
z: 1.0,
};
let int_unit_cube = Bounds3 {
p_min: int_origin,
p_max: int_xyz111,
};
let float_unit_cube = Bounds3 {
p_min: float_origin,
p_max: float_xyz111,
};

println!("int   {:?}", int_unit_cube);
println!("float {:?}", float_unit_cube);
}```

## Structs

 Bounds2 Bounds2Iterator Bounds3 Normal3 Point2 Point3 Ray RayDifferential Vector2 Vector3

## Functions

 bnd3_expand Pads the bounding box by a constant factor in both dimensions. bnd2_intersect_bnd2 The intersection of two bounding boxes can be found by computing the maximum of their two respective minimum coordinates and the minimum of their maximum coordinates. bnd3_union_bnd3 Construct a new box that bounds the space encompassed by two other bounding boxes. bnd3_union_pnt3 Given a bounding box and a point, the bnd3_union_pnt3() function returns a new bounding box that encompasses that point as well as the original box. nrm_abs Return normal with the absolute value of each coordinate. nrm_abs_dot_vec3 Computes the absolute value of the dot product. nrm_cross_vec3 Given a normal and a vector in 3D, the cross product is a vector that is perpendicular to both of them. nrm_dot_nrm Product of the Euclidean magnitudes of a normal (and another normal) and the cosine of the angle between them. A return value of zero means both are orthogonal, a value if one means they are codirectional. nrm_dot_vec3 Product of the Euclidean magnitudes of a normal (and a vector) and the cosine of the angle between them. A return value of zero means both are orthogonal, a value if one means they are codirectional. nrm_faceforward_nrm Flip a surface normal so that it lies in the same hemisphere as a given normal. nrm_faceforward_vec3 Flip a surface normal so that it lies in the same hemisphere as a given vector. pnt2_floor Apply floor operation component-wise. pnt2_ceil Apply ceil operation component-wise. pnt2_inside_exclusive Is a 2D point inside a 2D bound? pnt3_permute Permute the coordinate values according to the povided permutation. pnt3_lerp Interpolate linearly between two provided points. pnt3_floor Apply floor operation component-wise. pnt3_ceil Apply ceil operation component-wise. pnt3_abs Apply abs operation component-wise. pnt3_distance The distance between two points is the length of the vector between them. pnt3_distance_squared The distance squared between two points is the length of the vector between them squared. pnt3_offset_ray_origin When tracing spawned rays leaving the intersection point p, we offset their origins enough to ensure that they are past the boundary of the error box and thus won't incorrectly re-intersect the surface. pnt2_max_pnt2 Apply std::cmp::max operation component-wise. pnt2_min_pnt2 Apply std::cmp::min operation component-wise. pnt3_inside_bnd3 Determine if a given point is inside the bounding box. spherical_direction Calculate appropriate direction vector from two angles. spherical_direction_vec3 Take three basis vectors representing the x, y, and z axes and return the appropriate direction vector with respect to the coordinate frame defined by them. spherical_phi Conversion of a direction to spherical angles. spherical_theta Conversion of a direction to spherical angles. Note that spherical_theta() assumes that the vector v has been normalized before being passed in. vec2_dot Product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. A return value of zero means both vectors are orthogonal, a value if one means they are codirectional. vec3_dot_nrm Product of the Euclidean magnitudes of a vector (and a normal) and the cosine of the angle between them. A return value of zero means both are orthogonal, a value if one means they are codirectional. vec3_abs_dot_nrm Computes the absolute value of the dot product. vec3_cross_nrm Given a vectors and a normal in 3D, the cross product is a vector that is perpendicular to both of them. vec3_max_component Return the largest coordinate value. vec3_max_dimension Return the index of the component with the largest value. vec3_permute Permute the coordinate values according to the povided permutation. vec3_coordinate_system Construct a local coordinate system given only a single 3D vector. vec3_abs_dot_vec3 Computes the absolute value of the dot product. vec3_cross_vec3 Given two vectors in 3D, the cross product is a vector that is perpendicular to both of them. vec3_dot_vec3 Product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. A return value of zero means both vectors are orthogonal, a value if one means they are codirectional.

## Type Definitions

 Bounds2f Bounds2i Bounds3f Bounds3i Normal3f Point2f Point2i Point3f Point3i Vector2f Vector2i Vector3f Vector3i