Backport: Adding cone primitives. (#594)

Signed-off-by: Benjamin Perseghetti <bperseghetti@rudislabs.com>

Author: bperseghetti

include/gz/math/Cone.hh

@@ -0,0 +1,193 @@
+/*
+ * Copyright 2024 CogniPilot Foundation
+ * Copyright 2024 Open Source Robotics Foundation
+ * Copyright 2024 Rudis Laboratories
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+*/
+#ifndef GZ_MATH_CONE_HH_
+#define GZ_MATH_CONE_HH_
+
+#include <optional>
+#include "gz/math/MassMatrix3.hh"
+#include "gz/math/Material.hh"
+#include "gz/math/Quaternion.hh"
+
+namespace gz
+{
+  namespace math
+  {
+    // Foward declarations
+    class ConePrivate;
+
+    // Inline bracket to help doxygen filtering.
+    inline namespace GZ_MATH_VERSION_NAMESPACE {
+    //
+    /// \class Cone Cone.hh gz/math/Cone.hh
+    /// \brief A representation of a cone.
+    ///
+    /// The cone class supports defining a cone with a radius,
+    /// length, rotational offset, and material properties. Radius and
+    /// length are in meters. See Material for more on material properties.
+    /// By default, a cone's length is aligned with the Z axis where the base
+    /// of the cone is proximal to the origin and vertex points in positive Z.
+    /// The rotational offset encodes a rotation from the z axis.
+    template<typename Precision>
+    class Cone
+    {
+      /// \brief Default constructor. The default radius and length are both
+      /// zero. The default rotational offset is
+      /// Quaternion<Precision>::Identity.
+      public: Cone() = default;
+
+      /// \brief Construct a cone with a length, radius, and optionally
+      /// a rotational offset.
+      /// \param[in] _length Length of the cone.
+      /// \param[in] _radius Radius of the cone.
+      /// \param[in] _rotOffset Rotational offset of the cone.
+      public: Cone(const Precision _length, const Precision _radius,
+                   const Quaternion<Precision> &_rotOffset =
+                   Quaternion<Precision>::Identity);
+
+      /// \brief Construct a cone with a length, radius, material and
+      /// optionally a rotational offset.
+      /// \param[in] _length Length of the cone.
+      /// \param[in] _radius Radius of the cone.
+      /// \param[in] _mat Material property for the cone.
+      /// \param[in] _rotOffset Rotational offset of the cone.
+      public: Cone(const Precision _length, const Precision _radius,
+                   const Material &_mat,
+                   const Quaternion<Precision> &_rotOffset =
+                   Quaternion<Precision>::Identity);
+
+      /// \brief Get the radius in meters.
+      /// \return The radius of the cone in meters.
+      public: Precision Radius() const;
+
+      /// \brief Set the radius in meters.
+      /// \param[in] _radius The radius of the cone in meters.
+      public: void SetRadius(const Precision _radius);
+
+      /// \brief Get the length in meters.
+      /// \return The length of the cone in meters.
+      public: Precision Length() const;
+
+      /// \brief Set the length in meters.
+      /// \param[in] _length The length of the cone in meters.
+      public: void SetLength(const Precision _length);
+
+      /// \brief Get the rotational offset. By default, a cone's length
+      /// is aligned with the Z axis. The rotational offset encodes
+      /// a rotation from the z axis.
+      /// \return The cone's rotational offset.
+      /// \sa void SetRotationalOffset(const Quaternion<Precision> &_rot)
+      public: Quaternion<Precision> RotationalOffset() const;
+
+      /// \brief Set the rotation offset.
+      /// \param[in] _rotOffset rotational offset quaternion.
+      /// See Quaternion<Precision> RotationalOffset() for details on the
+      /// rotational offset.
+      /// \sa Quaternion<Precision> RotationalOffset() const
+      public: void SetRotationalOffset(
+                  const Quaternion<Precision> &_rotOffset);
+
+      /// \brief Get the material associated with this cone.
+      /// \return The material assigned to this cone
+      public: const Material &Mat() const;
+
+      /// \brief Set the material associated with this cone.
+      /// \param[in] _mat The material assigned to this cone
+      public: void SetMat(const Material &_mat);
+
+      /// \brief Get the mass matrix for this cone. This function
+      /// is only meaningful if the cone's radius, length, and material
+      /// have been set. Optionally, set the rotational offset.
+      /// \param[out] _massMat The computed mass matrix will be stored
+      /// here.
+      /// \return False if computation of the mass matrix failed, which
+      /// could be due to an invalid radius (<=0), length (<=0), or density
+      /// (<=0).
+      public: bool MassMatrix(MassMatrix3d &_massMat) const;
+
+      /// \brief Get the mass matrix for this cone. This function
+      /// is only meaningful if the cone's radius, length, and material
+      /// have been set. Optionally, set the rotational offset.
+      /// \return The computed mass matrix if parameters are valid
+      /// (radius > 0), (length > 0) and (density > 0). Otherwise
+      /// std::nullopt is returned.
+      public: std::optional< MassMatrix3<Precision> > MassMatrix() const;
+
+      /// \brief Check if this cone is equal to the provided cone.
+      /// Radius, length, and material properties will be checked.
+      public: bool operator==(const Cone &_cone) const;
+
+      /// \brief Get the volume of the cone in m^3.
+      /// \return Volume of the cone in m^3.
+      public: Precision Volume() const;
+
+      /// \brief Compute the cone's density given a mass value. The
+      /// cone is assumed to be solid with uniform density. This
+      /// function requires the cone's radius and length to be set to
+      /// values greater than zero. The Material of the cone is ignored.
+      /// \param[in] _mass Mass of the cone, in kg. This value should be
+      /// greater than zero.
+      /// \return Density of the cone in kg/m^3. A negative value is
+      /// returned if radius, length or _mass is <= 0.
+      public: Precision DensityFromMass(const Precision _mass) const;
+
+      /// \brief Set the density of this cone based on a mass value.
+      /// Density is computed using
+      /// Precision DensityFromMass(const Precision _mass) const. The
+      /// cone is assumed to be solid with uniform density. This
+      /// function requires the cone's radius and length to be set to
+      /// values greater than zero. The existing Material density value is
+      /// overwritten only if the return value from this true.
+      /// \param[in] _mass Mass of the cone, in kg. This value should be
+      /// greater than zero.
+      /// \return True if the density was set. False is returned if the
+      /// cone's radius, length, or the _mass value are <= 0.
+      /// \sa Precision DensityFromMass(const Precision _mass) const
+      public: bool SetDensityFromMass(const Precision _mass);
+
+      /// \brief Radius of the cone.
+      private: Precision radius = 0.0;
+
+      /// \brief Length of the cone.
+      private: Precision length = 0.0;
+
+      /// \brief the cone's material.
+      private: Material material;
+
+      /// \brief Rotational offset.
+      private: Quaternion<Precision> rotOffset =
+               Quaternion<Precision>::Identity;
+    };
+
+    /// \typedef Cone<int> Conei
+    /// \brief Cone with integer precision.
+    typedef Cone<int> Conei;
+
+    /// \typedef Cone<double> Coned
+    /// \brief Cone with double precision.
+    typedef Cone<double> Coned;
+
+    /// \typedef Cone<float> Conef
+    /// \brief Cone with float precision.
+    typedef Cone<float> Conef;
+    }
+  }
+}
+#include "gz/math/detail/Cone.hh"
+
+#endif

include/gz/math/Helpers.hh

@@ -67,6 +67,11 @@ constexpr T IGN_MASSMATRIX3_DEFAULT_TOLERANCE = T(10);
 /// \param[in] _radius Sphere radius
 #define GZ_SPHERE_VOLUME(_radius) (4.0*GZ_PI*std::pow(_radius, 3)/3.0)
 
+/// \brief Compute cone volume
+/// \param[in] _r Cone base radius
+/// \param[in] _l Cone length
+#define GZ_CONE_VOLUME(_r, _l) (_l * GZ_PI * std::pow(_r, 2) / 3.0)
+
 /// \brief Compute cylinder volume
 /// \param[in] _r Cylinder base radius
 /// \param[in] _l Cylinder length

include/gz/math/MassMatrix3.hh

@@ -18,6 +18,7 @@
 #define GZ_MATH_MASSMATRIX3_HH_
 
 #include <algorithm>
+#include <cmath>
 #include <limits>
 #include <string>
 #include <vector>
@@ -930,6 +931,85 @@ namespace gz
         return this->SetMoi(R * L * R.Transposed());
       }
 
+      /// \brief Set inertial properties based on a Material and equivalent
+      /// cone aligned with Z axis.
+      /// \param[in] _mat Material that specifies a density. Uniform density
+      /// is used.
+      /// \param[in] _length Length of cone along Z axis.
+      /// \param[in] _radius Radius of cone.
+      /// \param[in] _rot Rotational offset of equivalent cone.
+      /// \return True if inertial properties were set successfully.
+      public: bool SetFromConeZ(const Material &_mat,
+                                const T _length,
+                                const T _radius,
+                                const Quaternion<T> &_rot =
+                                Quaternion<T>::Identity)
+      {
+        // Check that density, _radius and _length are strictly positive
+        // and that quaternion is valid
+        if (_mat.Density() <= 0 || _length <= 0 || _radius <= 0 ||
+            _rot == Quaternion<T>::Zero)
+        {
+          return false;
+        }
+        T volume = GZ_PI * _radius * _radius * _length / 3.0;
+        return this->SetFromConeZ(_mat.Density() * volume,
+                                      _length, _radius, _rot);
+      }
+
+      /// \brief Set inertial properties based on mass and equivalent cone
+      /// aligned with Z axis.
+      /// \param[in] _mass Mass to set.
+      /// \param[in] _length Length of cone along Z axis.
+      /// \param[in] _radius Radius of cone.
+      /// \param[in] _rot Rotational offset of equivalent cone.
+      /// \return True if inertial properties were set successfully.
+      public: bool SetFromConeZ(const T _mass,
+                                const T _length,
+                                const T _radius,
+                                const Quaternion<T> &_rot =
+                                Quaternion<T>::Identity)
+      {
+        // Check that _mass, _radius and _length are strictly positive
+        // and that quaternion is valid
+        if (_mass <= 0 || _length <= 0 || _radius <= 0 ||
+            _rot == Quaternion<T>::Zero)
+        {
+          return false;
+        }
+        this->SetMass(_mass);
+        return this->SetFromConeZ(_length, _radius, _rot);
+      }
+
+      /// \brief Set inertial properties based on equivalent cone
+      /// aligned with Z axis using the current mass value.
+      /// \param[in] _length Length of cone along Z axis.
+      /// \param[in] _radius Radius of cone.
+      /// \param[in] _rot Rotational offset of equivalent cone.
+      /// \return True if inertial properties were set successfully.
+      public: bool SetFromConeZ(const T _length,
+                                const T _radius,
+                                const Quaternion<T> &_rot)
+      {
+        // Check that _mass and _size are strictly positive
+        // and that quaternion is valid
+        if (this->Mass() <= 0 || _length <= 0 || _radius <= 0 ||
+            _rot == Quaternion<T>::Zero)
+        {
+          return false;
+        }
+
+        // Diagonal matrix L with principal moments
+        T radius2 = std::pow(_radius, 2);
+        Matrix3<T> L;
+        L(0, 0) = 3.0 * this->mass * (4.0 * radius2 +
+                  std::pow(_length, 2)) / 80.0;
+        L(1, 1) = L(0, 0);
+        L(2, 2) = 3.0 * this->mass * radius2 / 10.0;
+        Matrix3<T> R(_rot);
+        return this->SetMoi(R * L * R.Transposed());
+      }
+
       /// \brief Set inertial properties based on a Material and equivalent
       /// cylinder aligned with Z axis.
       /// \param[in] _mat Material that specifies a density. Uniform density