Changeset 308 for trunk/src/random.cc

Timestamp:

08/12/14 20:34:31 (11 years ago)

Author:

epyon

Message:

• multiple heavy duty functions added for random uniform distribution on: circles spheres disks spheroids hollow versions of all of the above

File:

• trunk/src/random.cc (modified) (1 diff)

trunk/src/random.cc

@@ -90 +90 @@
         return narrow_cast< seed_type >( get_ticks() );
 }
+
+nv::vec2 nv::random::precise_unit_vec2()
+{
+        std::uniform_real_distribution<f32> dist( 0, glm::pi<float>() * 2.f );
+        float angle = dist( rng );
+        return vec2( glm::cos( angle ), glm::sin( angle ) );
+}
+
+nv::vec3 nv::random::precise_unit_vec3()
+{
+        std::uniform_real_distribution<f32> dist11( -1.0f, 1.0f );
+        std::uniform_real_distribution<f32> dist02pi( 0.0f, 2*glm::pi<float>() );
+        float cos_theta = dist11( rng );
+        float sin_theta = glm::sqrt( 1.0f - cos_theta * cos_theta );
+        float phi       = dist02pi( rng );
+        return vec3( 
+                sin_theta * glm::sin(phi),
+                sin_theta * glm::cos(phi),
+                cos_theta
+                );
+}
+
+nv::vec2 nv::random::fast_disk_point()
+{
+        std::uniform_real_distribution<f32> dist( 0.0f, 1.0f );
+        float r1 = dist( rng );
+        float r2 = dist( rng );
+        if ( r1 > r2 ) std::swap( r1, r2 );
+        float rf = 2*glm::pi<float>()*(r1/r2);
+        return vec2( r2*glm::cos( rf ), r2*glm::sin( rf ) );
+}
+
+nv::vec2 nv::random::precise_disk_point()
+{
+        std::uniform_real_distribution<f32> unit( 0.0f, 1.0f );
+        std::uniform_real_distribution<f32> angle( 0.0f, glm::pi<float>() );
+        float r = glm::sqrt( unit( rng ) );
+        float rangle = angle( rng );
+        return vec2( r*glm::cos( rangle ), r*glm::sin( rangle ) );
+}
+
+nv::vec3 nv::random::fast_sphere_point()
+{
+        std::uniform_real_distribution<f32> dist01( 0.0f, 1.0f );
+        std::uniform_real_distribution<f32> dist11( -1.0f, 1.0f );
+        std::uniform_real_distribution<f32> dist02pi( 0.0f, 2*glm::pi<float>() );
+        float rad     = dist01( rng );
+        float pi      = glm::pi<float>();
+        float phi     = glm::asin( dist11( rng ) ) + pi*.5f;
+        float theta   = dist02pi( rng );
+        float sin_phi = glm::sin( phi );
+        return vec3( 
+                rad * glm::cos(theta) * sin_phi,
+                rad * glm::sin(theta) * sin_phi,
+                rad * glm::cos(phi)
+        );
+}
+
+nv::vec3 nv::random::precise_sphere_point()
+{
+        std::uniform_real_distribution<f32> dist01( 0.0f, 1.0f );
+        std::uniform_real_distribution<f32> dist11( -1.0f, 1.0f );
+        std::uniform_real_distribution<f32> dist02pi( 0.0f, 2*glm::pi<float>() );
+        float radius = std::pow( dist01( rng ), 1.f/3.f );
+        float cos_theta = dist11( rng );
+        float sin_theta = glm::sqrt( 1.0f - cos_theta * cos_theta );
+        float phi       = dist02pi( rng );
+        return vec3( 
+                radius * sin_theta * glm::sin(phi),
+                radius * sin_theta * glm::cos(phi),
+                radius * cos_theta
+                );
+}
+
+nv::vec2 nv::random::precise_ellipse_point( const vec2& radii )
+{
+        std::uniform_real_distribution<f32> distx( -radii.x, radii.x );
+        std::uniform_real_distribution<f32> disty( -radii.y, radii.y );
+        vec2 inv_radii  = 1.f / radii;
+        vec2 inv_radii2 = inv_radii * inv_radii;
+        for ( uint32 i = 0; i < 12; ++i )
+        {
+                float x = distx( rng );
+                float y = disty( rng );
+                if ( x * x * inv_radii2.x + y * y * inv_radii2.y <= 1.f )
+                {
+                        return vec2( x, y );
+                }
+        }
+        return fast_disk_point() * radii;
+}
+
+nv::vec3 nv::random::precise_ellipsoid_point( const vec3& radii )
+{
+        std::uniform_real_distribution<f32> distx( -radii.x, radii.x );
+        std::uniform_real_distribution<f32> disty( -radii.y, radii.y );
+        std::uniform_real_distribution<f32> distz( -radii.z, radii.z );
+        vec3 inv_radii  = 1.f / radii;
+        vec3 inv_radii2 = inv_radii * inv_radii;
+        for ( uint32 i = 0; i < 12; ++i )
+        {
+                float x = distx( rng );
+                float y = disty( rng );
+                float z = distz( rng );
+                if ( x * x * inv_radii2.x + y * y * inv_radii2.y + z * z * inv_radii2.z <= 1.f )
+                {
+                        return vec3( x, y, z );
+                }
+        }
+        return fast_sphere_point() * radii;
+}
+
+nv::vec2 nv::random::fast_hollow_disk_point( float iradius, float oradius )
+{
+        float idist2 = iradius * iradius;
+        float odist2 = oradius * oradius;
+        float rdist  = glm::sqrt( std::uniform_real_distribution<f32>( idist2, odist2 )( rng ) );
+        return rdist * precise_unit_vec2();
+}
+
+nv::vec2 nv::random::precise_hollow_disk_point( float iradius, float oradius )
+{
+        return fast_hollow_disk_point( iradius, oradius );
+}
+
+nv::vec3 nv::random::fast_hollow_sphere_point( float iradius, float oradius )
+{
+        float idist3 = iradius * iradius * iradius;
+        float odist3 = oradius * oradius * oradius;
+        float rdist  = std::pow( std::uniform_real_distribution<f32>( idist3, odist3 )( rng ), 1.f/3.f );
+        return rdist * precise_unit_vec3();
+}
+
+nv::vec3 nv::random::precise_hollow_sphere_point( float iradius, float oradius )
+{
+        return fast_hollow_sphere_point( iradius, oradius );
+}
+
+
+nv::vec2 nv::random::fast_hollow_ellipse_point( const vec2& iradii, const vec2& oradii )
+{
+        vec2 iradii2    = iradii * iradii;
+        vec2 opoint     = ellipse_edge( oradii );
+        vec2 opoint2    = opoint * opoint;
+        vec2 odir       = glm::normalize( opoint );
+        float odist2    = opoint2.x + opoint2.y;
+
+        float low    = iradii2.y * opoint2.x + iradii2.x * opoint2.y;
+        float idist2 = ((iradii2.x * iradii2.y) / low ) * odist2;
+
+        float rdist     = glm::sqrt( std::uniform_real_distribution<f32>( idist2, odist2 )( rng ) );
+        return odir * rdist;    
+}
+
+nv::vec2 nv::random::precise_hollow_ellipse_point( const vec2& iradii, const vec2& oradii )
+{
+        return fast_hollow_ellipse_point( iradii, oradii );
+}
+
+nv::vec3 nv::random::fast_hollow_ellipsoid_point( const vec3& iradii, const vec3& oradii )
+{
+        vec3 iradii2    = iradii * iradii;
+        vec3 opoint     = ellipsoid_edge( oradii );
+        vec3 opoint2    = opoint * opoint;
+        vec3 odir       = glm::normalize( opoint );
+        float odist2    = opoint2.x + opoint2.y + opoint2.z;
+
+        float low    = 
+                iradii2.y * iradii2.z * opoint2.x + 
+                iradii2.x * iradii2.z * opoint2.y +
+                iradii2.x * iradii2.y * opoint2.z;
+        float idist2 = ((iradii2.x * iradii2.y * iradii2.z) / low ) * odist2;
+
+        float odist3 = odist2 * glm::sqrt( odist2 );
+        float idist3 = idist2 * glm::sqrt( idist2 );
+
+        float rdist     = std::pow( std::uniform_real_distribution<f32>( idist3, odist3 )( rng ), 1.f/3.f );
+        return odir * rdist;    
+}
+
+nv::vec3 nv::random::precise_hollow_ellipsoid_point( const vec3& iradii, const vec3& oradii )
+{
+        return fast_hollow_ellipsoid_point( iradii, oradii );
+}
+