pointGeneration.h

/*
This Source Code Form is subject to the terms of the Mozilla Public
 License, v. 2.0. If a copy of the MPL was not distributed with this
 file, You can obtain one at http://mozilla.org/MPL/2.0/.
*/
 
#pragma once
 
#include "Eigen/Eigen"
#include "./defines.h"
#include "./concepts.h"
 
#define MIN_NOISE 0.99
#define MAX_NOISE 1.01
 
namespace Ponca
{
 
    template <typename DataPoint>
    [[nodiscard]] DataPoint getPointOnSphere(const typename DataPoint::Scalar _radius,
                                             const typename DataPoint::VectorType _vCenter,
                                             const bool _bAddPositionNoise = true, const bool _bAddNormalNoise = true,
                                             const bool _bReverseNormals = false)
    {
        using Scalar     = typename DataPoint::Scalar;
        using VectorType = typename DataPoint::VectorType;
 
        VectorType vNormal   = VectorType::Random().normalized();
        VectorType vPosition = _vCenter + vNormal * _radius;
 
        if (_bAddPositionNoise)
        {
            vPosition = vPosition + VectorType::Random().normalized() *
                                        Eigen::internal::random<Scalar>(Scalar(0.), Scalar(1. - MIN_NOISE));
            vNormal = (vPosition - _vCenter).normalized();
        }
 
        if (_bAddNormalNoise)
        {
            VectorType vTempPos = vPosition + VectorType::Random().normalized() *
                                                  Eigen::internal::random<Scalar>(Scalar(0.), Scalar(1. - MIN_NOISE));
            vNormal = (vTempPos - _vCenter).normalized();
        }
        if (_bReverseNormals)
        {
            const float reverse = Eigen::internal::random<float>(0.f, 1.f);
            if (reverse > 0.5f)
                vNormal = -vNormal;
        }
 
        return DataPoint(vPosition, vNormal);
    }
 
    template <typename VectorType>
    [[nodiscard]] VectorType getPointOnCircle(typename VectorType::Scalar _radius, VectorType _vCenter)
    {
        using Scalar = typename VectorType::Scalar;
        // Generate random angle
        const Scalar theta = Eigen::internal::random<Scalar>(0, Scalar(2. * EIGEN_PI));
 
        // Generate random radius (adjusted for uniform area distribution)
        const Scalar r = _radius * std::sqrt(Eigen::internal::random<Scalar>(0, 1));
 
        // Convert to Cartesian coordinates
        VectorType p = _vCenter;
        p.x() += r * std::cos(theta);
        p.y() += r * std::sin(theta);
 
        return p;
    }
 
    template <typename DataPoint>
    [[nodiscard]] DataPoint getPointOnRectangularPlane(const typename DataPoint::VectorType& _vPosition,
                                                       const typename DataPoint::VectorType& /*_vNormal*/,
                                                       const typename DataPoint::Scalar& _width,
                                                       const typename DataPoint::Scalar& _height,
                                                       const typename DataPoint::VectorType& _localxAxis,
                                                       const typename DataPoint::VectorType& _localyAxis,
                                                       const bool _bAddPositionNoise = true)
    {
        using Scalar     = typename DataPoint::Scalar;
        using VectorType = typename DataPoint::VectorType;
 
        const Scalar u = Eigen::internal::random<Scalar>(-_width / Scalar(2), _width / Scalar(2));
        const Scalar v = Eigen::internal::random<Scalar>(-_height / Scalar(2), _height / Scalar(2));
 
        VectorType vRandomPosition = _vPosition + u * _localxAxis + v * _localyAxis;
 
        if (_bAddPositionNoise)
        {
            vRandomPosition = vRandomPosition +
                              VectorType::Random().normalized() * Eigen::internal::random<Scalar>(0., 1. - MIN_NOISE);
        }
 
        return DataPoint(vRandomPosition);
    }
 
    template <typename DataPoint>
    [[nodiscard]] DataPoint getPointOnPlane(const typename DataPoint::VectorType _vPosition,
                                            const typename DataPoint::VectorType _vNormal,
                                            const typename DataPoint::Scalar _radius,
                                            const bool _bAddPositionNoise = true, const bool _bAddNormalNoise = true,
                                            const bool _bReverseNormals = false)
    {
        using Scalar         = typename DataPoint::Scalar;
        using VectorType     = typename DataPoint::VectorType;
        using QuaternionType = Eigen::Quaternion<Scalar>;
 
        VectorType vRandom;
        VectorType vRandomDirection = VectorType::Zero();
        VectorType vRandomPoint     = VectorType::Zero();
        VectorType vLocalUp         = _vNormal;
 
        do
        {
            vRandom          = VectorType::Random().normalized(); // Direction in the unit sphere
            vRandomDirection = vRandom.cross(vLocalUp);
        } while (vRandomDirection == VectorType::Zero());
 
        vRandomDirection = vRandomDirection.normalized();
        vRandomPoint     = vRandomDirection * _radius;
        vRandomPoint += _vPosition;
 
        if (_bAddPositionNoise)
        {
            vRandomPoint = vRandomPoint + VectorType::Random().normalized() *
                                              Eigen::internal::random<Scalar>(Scalar(0), Scalar(1. - MIN_NOISE));
        }
 
        if (_bAddNormalNoise)
        {
            VectorType vLocalLeft  = vLocalUp.cross(vRandomDirection);
            VectorType vLocalFront = vLocalLeft.cross(vLocalUp);
 
            Scalar rotationAngle     = Eigen::internal::random<Scalar>(Scalar(-M_PI / 16.), Scalar(M_PI / 16.));
            VectorType vRotationAxis = vLocalLeft;
            QuaternionType qRotation = QuaternionType(Eigen::AngleAxis<Scalar>(rotationAngle, vRotationAxis));
            qRotation                = qRotation.normalized();
            vLocalUp                 = qRotation * vLocalUp;
 
            rotationAngle = Eigen::internal::random<Scalar>(Scalar(-M_PI / 16.), Scalar(M_PI / 16.));
            vRotationAxis = vLocalFront;
            qRotation     = QuaternionType(Eigen::AngleAxis<Scalar>(rotationAngle, vRotationAxis));
            qRotation     = qRotation.normalized();
            vLocalUp      = qRotation * vLocalUp;
        }
 
        if (_bReverseNormals)
        {
            const float reverse = Eigen::internal::random<float>(0.f, 1.f);
            if (reverse > 0.5f)
                vLocalUp = -vLocalUp;
        }
 
        return DataPoint(vRandomPoint, vLocalUp);
    }
 
    namespace internal
    {
        template <typename Scalar>
        [[nodiscard]] inline Scalar getParaboloidZ(const Scalar _x, const Scalar _y, const Scalar _a, const Scalar _b)
        {
            return _a * _x * _x + _b * _y * _y;
        }
 
        template <typename Scalar>
        [[nodiscard]] inline Scalar getParaboloidZ(Scalar _x, Scalar _y, Scalar _a, Scalar _b, Scalar _c, Scalar _d,
                                                   Scalar _e, Scalar _f)
        {
            return _a * _x * _x + _b * _y * _y + _c * _x * _y + _d * _x + _e * _y + _f;
        }
 
        template <typename VectorType>
        [[nodiscard]] inline VectorType getParaboloidNormal(const VectorType& in, const typename VectorType::Scalar _a,
                                                            const typename VectorType::Scalar _b)
        {
            return VectorType((_a * in.x()), (_b * in.y()), -1.).normalized();
            ;
        }
        template <IsPointNormal DataPoint>
        inline void getParaboloidNormal(DataPoint& in, typename DataPoint::Scalar _a, typename DataPoint::Scalar _b,
                                        typename DataPoint::Scalar _c, typename DataPoint::Scalar _d,
                                        typename DataPoint::Scalar _e, typename DataPoint::Scalar _f)
        {
            static constexpr typename DataPoint::Scalar two{2};
            auto& pos   = in.pos();
            in.normal() = typename DataPoint::VectorType(two * _a * pos.x() + _c * pos.y() + _d,
                                                         two * _b * pos.y() + _c * pos.x() + _d, -1.)
                              .normalized();
        }
    } // namespace internal
 
    template <typename DataPoint>
    [[nodiscard]] DataPoint getPointOnParaboloid(const typename DataPoint::Scalar _a,
                                                 const typename DataPoint::Scalar _b,
                                                 const typename DataPoint::Scalar _s, const bool _bAddNoise = true)
    {
        using Scalar     = typename DataPoint::Scalar;
        using VectorType = typename DataPoint::VectorType;
 
        VectorType vNormal;
        VectorType vPosition;
 
        const Scalar x = Eigen::internal::random<Scalar>(-_s, _s), y = Eigen::internal::random<Scalar>(-_s, _s);
 
        vPosition = {x, y, internal::getParaboloidZ(x, y, _a, _b)};
        vNormal   = internal::getParaboloidNormal(vPosition, _a, _b);
 
        if (_bAddNoise) // spherical noise
            vPosition +=
                VectorType::Random().normalized() * Eigen::internal::random<Scalar>(Scalar(0), Scalar(1. - MIN_NOISE));
 
        return DataPoint(vPosition, vNormal);
    }
 
    template <typename DataPoint>
    [[nodiscard]] DataPoint getPointOnParaboloid(typename DataPoint::Scalar _a, typename DataPoint::Scalar _b,
                                                 typename DataPoint::Scalar _c, typename DataPoint::Scalar _d,
                                                 typename DataPoint::Scalar _e, typename DataPoint::Scalar _f,
                                                 typename DataPoint::Scalar _s, bool _bAddNoise = true)
    {
        using Scalar     = typename DataPoint::Scalar;
        using VectorType = typename DataPoint::VectorType;
 
        DataPoint out;
 
        // generate random position in polar coordinates to get points on the circle
        out.pos()     = getPointOnCircle(_s, VectorType({0, 0, 0}));
        out.pos().z() = internal::getParaboloidZ(out.pos().x(), out.pos().y(), _a, _b, _c, _d, _e, _f);
 
        // does nothing if the point type does not have a normal field.
        internal::getParaboloidNormal(out, _a, _b, _c, _d, _e, _f);
 
        if (_bAddNoise) // spherical noise
        {
            out.pos() +=
                VectorType::Random().normalized() * Eigen::internal::random<Scalar>(Scalar(0), Scalar(1. - MIN_NOISE));
        }
 
        return out;
    }
 
    template <typename DataPoint, typename Params>
    [[nodiscard]] DataPoint getPointOnParaboloid(const Params& _params, typename DataPoint::Scalar _s,
                                                 bool _bAddNoise = true)
    {
        return getPointOnParaboloid<DataPoint>(_params(0), _params(1), _params(2), _params(3), _params(4), _params(5),
                                               _s, _bAddNoise);
    }
 
    template <typename DataPoint>
    [[nodiscard]] DataPoint getRandomPoint()
    {
        using Scalar       = typename DataPoint::Scalar;
        using VectorType   = typename DataPoint::VectorType;
        const VectorType n = VectorType::Random().normalized();
        const VectorType p = n * Eigen::internal::random<Scalar>(MIN_NOISE, MAX_NOISE);
        return {p, (n + VectorType::Random() * Scalar(0.1)).normalized()};
    }
} // namespace Ponca