Philip-Trettner / probabilistic-quadrics

Reference implementation of the Eurographics 2020 paper "Fast and Robust QEF Minimization using Probabilistic Quadrics"

Probabilistic Quadrics

Reference implementation of the Eurographics 2020 paper "Fast and Robust QEF Minimization using Probabilistic Quadrics".

• Publication page: https://graphics.rwth-aachen.de/probabilistic-quadrics
• Eurographics DL: https://diglib.eg.org/handle/10.1111/cgf13933
• Eurographics Talk: https://www.youtube.com/watch?v=uEzGgFdbFMA&t=3080s

@article {10.1111:cgf.13933,
    journal = {Computer Graphics Forum},
    title = {{Fast and Robust QEF Minimization using Probabilistic Quadrics}},
    author = {Trettner, Philip and Kobbelt, Leif},
    year = {2020},
    publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/cgf.13933}
}

Dependencies

• a C++17 compiler

Usage

// our probabilistic quadrics
#include "probabilistic-quadrics.hh"

// some math library (see below for different options)
#include "minimal-math.hh"

// optional: typedef your quadric type
using quadric3 = pq::quadric<pq::minimal_math<float>>;
using dquadric3 = pq::quadric<pq::minimal_math<double>>;

// quadrics are value types with proper operator overloads
quadric3 q;
q = q + q;
q = q - q;
q = q * 3;
q = q / 2.5f;

// quadrics can be evaluated at positions
q(1, 2, 3);
q({1, 2, 3});
q(some_pos);

// quadrics can be created from coefficients
q = quadric3::from_coefficients(some_mat3, some_vec3, some_scalar);

// quadric minimizers can be computed (using matrix inversion internally)
pq::pos3 min_p = q.minimizer();

// some classical quadrics are predefined:
q = quadric3::point_quadric(some_pos);
q = quadric3::plane_quadric(some_pos, some_normal_vec);
q = quadric3::triangle_quadric(p0, p1, p2);

// our probabilistic plane quadrics in isotropic or general form:
float stddev_pos = ...;
float stddev_normal = ...;
pq:mat3 sigma_pos = ...;
pq:mat3 sigma_normal = ...;
q = quadric3::probabilistic_plane_quadric(mean_pos, mean_normal, stddev_pos, stddev_normal);
q = quadric3::probabilistic_plane_quadric(mean_pos, mean_normal, sigma_pos, sigma_normal);

// our probabilistic triangle quadrics in isotropic or general form:
float stddev_pos = ...;
pq:mat3 sigma_p0 = ...;
pq:mat3 sigma_p1 = ...;
pq:mat3 sigma_p2 = ...;
q = quadric3::probabilistic_triangle_quadric(p0, p1, p2, stddev_pos);
q = quadric3::probabilistic_triangle_quadric(p0, p1, p2, sigma_p0, sigma_p1, sigma_p2);

Math Class

Our code is written to be largely agnostic to the choice of the math library. The quadric type is templated on a trait class that abstracts the math code away. Different types for positions and vectors are supported but not required.

template <class ScalarT, class Pos3, class Vec3, class Mat3>
struct math;

The following math classes are tested:

• the built-in minimal-math.hh:

  #include "minimal-math.hh"
  pq::minimal_math<float>
  pq::minimal_math<double>

• Typed Geometry:

  #include <typed-geometry/tg.hh>
  pq::math<float, tg::pos3, tg::vec3, tg::mat3>
  pq::math<double, tg::dpos3, tg::dvec3, tg::dmat3>

• GLM:

  #include <glm/glm.hpp>
  pq::math<float, glm::vec3, glm::vec3, glm::mat3>
  pq::math<double, glm::dvec3, glm::dvec3, glm::dmat3>

• Eigen:

  #include <eigen3/Eigen/Core>
  pq::math<float, Eigen::Vector3f, Eigen::Vector3f, Eigen::Matrix3f>
  pq::math<double, Eigen::Vector3d, Eigen::Vector3d, Eigen::Matrix3d>

To make your custom math library work, it needs to provide the following operations:

• pos - pos -> vec
• pos + vec -> pos
• pos - vec -> pos
• vec + vec -> vec
• vec - vec -> vec
• vec * scalar -> vec
• vec / scalar -> vec
• pos * scalar -> pos
• pos / scalar -> pos
• mat * scalar -> mat
• mat * vec -> vec
• mat + mat -> mat
• mat - mat -> mat
• pos[int-literal] -> scalar&
• vec[int-literal] -> scalar&
• mat[col][row] -> scalar& OR mat(row, col) -> scalar&
• mat, pos and vec default constructor
• mat, pos, vec, and scalar behave like value types
• scalar must be constructable from integer literals where
• pos is a 3D position type
• vec is a 3D vector type
• pos and vec can be the same, e.g. glm::vec3
• mat is a 3x3 matrix type

License

This code is licensed under the MIT license.