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/*
* // Copyright (c) 2021 Feng Yang
* //
* // I am making my contributions/submissions to this project solely in my
* // personal capacity and am not conveying any rights to any intellectual
* // property of any third parties.
*/
use crate::vector3::Vector3D;
use num::traits::Pow;
///
/// # Standard 3-D SPH kernel function object.
///
/// \see Müller, Matthias, David Charypar, and Markus Gross.
/// "Particle-based fluid simulation for interactive applications."
/// Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer
/// animation. Eurographics Association, 2003.
///
pub struct SphStdKernel3 {
/// Kernel radius.
pub h: f64,
/// Square of the kernel radius.
pub h2: f64,
/// Cubic of the kernel radius.
pub h3: f64,
/// Fifth-power of the kernel radius.
pub h5: f64,
}
impl SphStdKernel3 {
/// Constructs a kernel object with zero radius.
pub fn new_default() -> SphStdKernel3 {
return SphStdKernel3 {
h: 0.0,
h2: 0.0,
h3: 0.0,
h5: 0.0,
};
}
/// Constructs a kernel object with given radius.
pub fn new(kernel_radius: f64) -> SphStdKernel3 {
return SphStdKernel3 {
h: kernel_radius,
h2: kernel_radius.pow(2),
h3: kernel_radius.pow(3),
h5: kernel_radius.pow(5),
};
}
/// Returns kernel function value at given distance.
pub fn apply(&self, distance: f64) -> f64 {
return if distance * distance >= self.h2 {
0.0
} else {
let x = 1.0 - distance * distance / self.h2;
315.0 / (64.0 * crate::constants::K_PI_D * self.h3) * x * x * x
};
}
/// Returns the first derivative at given distance.
pub fn first_derivative(&self, distance: f64) -> f64 {
return if distance >= self.h {
0.0
} else {
let x = 1.0 - distance * distance / self.h2;
-945.0 / (32.0 * crate::constants::K_PI_D * self.h5) * distance * x * x
};
}
/// Returns the gradient at a point.
pub fn gradient_pnt(&self, point: &Vector3D) -> Vector3D {
let dist = point.length();
return if dist > 0.0 {
self.gradient_dir(dist, &(*point / dist))
} else {
Vector3D::new_default()
};
}
/// Returns the gradient at a point defined by distance and direction.
pub fn gradient_dir(&self, distance: f64, direction: &Vector3D) -> Vector3D {
return *direction * -self.first_derivative(distance);
}
/// Returns the second derivative at given distance.
pub fn second_derivative(&self, distance: f64) -> f64 {
return if distance * distance >= self.h2 {
0.0
} else {
let x = distance * distance / self.h2;
945.0 / (32.0 * crate::constants::K_PI_D * self.h5) * (1.0 - x) * (5.0 * x - 1.0)
};
}
}
///
/// # Spiky 3-D SPH kernel function object.
///
/// \see Müller, Matthias, David Charypar, and Markus Gross.
/// "Particle-based fluid simulation for interactive applications."
/// Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer
/// animation. Eurographics Association, 2003.
///
pub struct SphSpikyKernel3 {
/// Kernel radius.
pub h: f64,
/// Square of the kernel radius.
pub h2: f64,
/// Cubic of the kernel radius.
pub h3: f64,
/// Fourth-power of the kernel radius.
pub h4: f64,
/// Fifth-power of the kernel radius.
pub h5: f64,
}
impl SphSpikyKernel3 {
/// Constructs a kernel object with zero radius.
pub fn new_default() -> SphSpikyKernel3 {
return SphSpikyKernel3 {
h: 0.0,
h2: 0.0,
h3: 0.0,
h4: 0.0,
h5: 0.0,
};
}
/// Constructs a kernel object with given radius.
pub fn new(kernel_radius: f64) -> SphSpikyKernel3 {
return SphSpikyKernel3 {
h: kernel_radius,
h2: kernel_radius.pow(2),
h3: kernel_radius.pow(3),
h4: kernel_radius.pow(4),
h5: kernel_radius.pow(5),
};
}
/// Returns kernel function value at given distance.
pub fn apply(&self, distance: f64) -> f64 {
return if distance >= self.h {
0.0
} else {
let x = 1.0 - distance / self.h;
15.0 / (crate::constants::K_PI_D * self.h3) * x * x * x
};
}
/// Returns the first derivative at given distance.
pub fn first_derivative(&self, distance: f64) -> f64 {
return if distance >= self.h {
0.0
} else {
let x = 1.0 - distance / self.h;
-45.0 / (crate::constants::K_PI_D * self.h4) * x * x
};
}
/// Returns the gradient at a point.
pub fn gradient_pnt(&self, point: &Vector3D) -> Vector3D {
let dist = point.length();
return if dist > 0.0 {
self.gradient_dir(dist, &(*point / dist))
} else {
Vector3D::new_default()
};
}
/// Returns the gradient at a point defined by distance and direction.
pub fn gradient_dir(&self, distance: f64, direction: &Vector3D) -> Vector3D {
return *direction * -self.first_derivative(distance);
}
/// Returns the second derivative at given distance.
pub fn second_derivative(&self, distance: f64) -> f64 {
return if distance >= self.h {
0.0
} else {
let x = 1.0 - distance / self.h;
90.0 / (crate::constants::K_PI_D * self.h5) * x
};
}
}