EllipticalManifold<dim, spacedim>::EllipticalManifold(
const Point<spacedim> & center,
const Tensor<1, spacedim> &major_axis_direction,
- const double c_parameter)
+ const double eccentricity)
: ChartManifold<dim, spacedim, spacedim>(
EllipticalManifold<dim, spacedim>::get_periodicity())
, direction(major_axis_direction)
, center(center)
- , c_parameter(c_parameter)
+ , cosh_u(1.0 / eccentricity)
+ , sinh_u(std::sqrt(cosh_u * cosh_u - 1.0))
{
- // throws an exception if dim!=2 || spacedim!=2.
+ // Throws an exception if dim!=2 || spacedim!=2.
Assert(dim == 2 && spacedim == 2, ExcNotImplemented());
- Assert(this->c_parameter > 0.0,
+ // Throws an exception if eccentricity is not in range.
+ Assert(std::signbit(cosh_u * cosh_u - 1.0) == false,
ExcMessage(
- "Invalid ellipsis parameter 'c': It must satisfy c > 0.0."));
+ "Invalid eccentricity: It must satisfy 0 < eccentricity < 1."));
const double direction_norm = direction.norm();
Assert(direction_norm != 0.0,
ExcMessage(
std::unique_ptr<Manifold<dim, spacedim>>
EllipticalManifold<dim, spacedim>::clone() const
{
- return std::make_unique<EllipticalManifold<dim, spacedim>>(center,
- direction,
- c_parameter);
+ const double eccentricity = 1.0 / cosh_u;
+ return std_cxx14::make_unique<EllipticalManifold<dim, spacedim>>(
+ center, direction, eccentricity);
}
Point<2>
EllipticalManifold<2, 2>::push_forward(const Point<2> &chart_point) const
{
- const double ch = std::cosh(chart_point[0]);
- const double sh = std::sinh(chart_point[0]);
const double cs = std::cos(chart_point[1]);
const double sn = std::sin(chart_point[1]);
// Coordinates in the reference frame (i.e. major axis direction is
// x-axis)
- const double x = c_parameter * ch * cs;
- const double y = c_parameter * sh * sn;
+ const double x = chart_point[0] * cosh_u * cs;
+ const double y = chart_point[0] * sinh_u * sn;
// Rotate them according to the major axis direction
const Point<2> p(direction[0] * x - direction[1] * y,
direction[1] * x + direction[0] * y);
EllipticalManifold<2, 2>::pull_back(const Point<2> &space_point) const
{
// Moving space_point in the reference coordinate system.
- const double c2 = c_parameter * c_parameter;
const double x0 = space_point[0] - center[0];
const double y0 = space_point[1] - center[1];
const double x = direction[0] * x0 + direction[1] * y0;
const double y = -direction[1] * x0 + direction[0] * y0;
- // From here we try to find solutions of two equations:
- // x^2/(1-q)-y^2/q = c^2 for q, given q = -sinh^2(pt[0]),
- // and
- // x^2/(1-p)-y^2/p = c^2 for p, given p = sin^2(pt[1]).
- // Note that, in the end, p and q are solutions to the same quadratic
- // equation.
- const double x2 = x * x;
- const double y2 = y * y;
- //
- const double b = x2 + y2 - c2;
- const double srdelta = std::sqrt(b * b + 4.0 * c2 * y2);
- double p = (-b + srdelta) / (2.0 * c2);
- // Since p=sin^2(pt[1]) is bounded in [0,1],
- // guard against numerical overflows.
- if (p < 0.0)
- p = 0.0;
- if (p > 1.0)
- p = 1.0;
- const double q = (-b - srdelta) / (2.0 * c2);
- const bool x_is_positive = !std::signbit(x);
- const bool y_is_positive = !std::signbit(y);
- const double eta0 = std::asin(std::sqrt(p));
- // Given q = -sinh^2(pt[0]),
- // pt[0] is calculated by straight inversion since q <= 0 for any
- // pt[0].
- Point<2> pt(std::log(std::sqrt(-q) + std::sqrt(1.0 - q)), eta0);
- // Unfolding pt[1] according to the quadrant.
- if (x_is_positive && !y_is_positive)
- pt[1] = 2.0 * numbers::PI - eta0;
- else if (!x_is_positive && y_is_positive)
- pt[1] = numbers::PI - eta0;
- else if (!x_is_positive && !y_is_positive)
- pt[1] = numbers::PI + eta0;
- return pt;
+ const double pt0 =
+ std::sqrt((x * x) / (cosh_u * cosh_u) + (y * y) / (sinh_u * sinh_u));
+ // If the radius is exactly zero, the point coincides with the origin.
+ if (pt0 == 0.0)
+ {
+ return center;
+ }
+ double cos_eta = x / (pt0 * cosh_u);
+ if (cos_eta < -1.0)
+ {
+ cos_eta = -1.0;
+ }
+ if (cos_eta > 1.0)
+ {
+ cos_eta = 1.0;
+ }
+ const double eta = std::acos(cos_eta);
+ const double pt1 = (std::signbit(y) ? 2.0 * numbers::PI - eta : eta);
+ return Point<2>(pt0, pt1);
}
EllipticalManifold<2, 2>::push_forward_gradient(
const Point<2> &chart_point) const
{
- const double ch = std::cosh(chart_point[0]);
- const double sh = std::sinh(chart_point[0]);
const double cs = std::cos(chart_point[1]);
const double sn = std::sin(chart_point[1]);
DerivativeForm<1, 2, 2> dX;
- dX[0][0] = c_parameter * sh * cs;
- dX[0][1] = -c_parameter * ch * sn;
- dX[1][0] = c_parameter * ch * sn;
- dX[1][1] = c_parameter * sh * cs;
+ dX[0][0] = cosh_u * cs;
+ dX[0][1] = -chart_point[0] * cosh_u * sn;
+ dX[1][0] = sinh_u * sn;
+ dX[1][1] = chart_point[1] * sinh_u * cs;
return dX;
}
// hyper_shell made of 8 elements.
namespace
{
- /* The following system of equations
- // /
- // |x = ellPar*cosh(u)*cos(v)
- // |y = ellPar*sinh(u)*sin(v)
- // \
- // allows to transform a point (u,v) in the chart space to a
- // point (x,y) in the cartesian space.
- //
- // Setting v=0, the system of equations becomes
- // /
- // |x = x_0 = ellPar*cosh(u)
- // |y = 0
- // \
- // which represents the crossing point of an ellipsis, non-rotated and
- // centered at the origin of the cartesian system, with its major axis.
- //
- // For the sake of completeness, by setting v=pi/2, one finds y_0 =
- // ellPar*sinh(u) as the crossing point on the minor axis.
- //
- // This function takes in input a point pt={x_0,v}
- // and transforms it into (x,y) in accordance with the first system of
- // equations above.
- //
- // On a final note, the condition x_0 >= ellPar has to be satisfied. This is
- // required because min(cosh(u)) = 1 is obtained for u = 0, and imposing v = 0
- // the minimum value that x can assume is x = ellPar.
- // For the sake of completeness, it's worth to notice that there would be no
- // restrictions on the input if we passed y_0, instead of x_0, as pt[0].
- */
- Point<2>
- chart_to_cartesian(const Point<2> &pt, const double ellPar)
- {
- Point<2> c;
- const double ch = pt[0] / ellPar;
- const double sh = std::sqrt(ch * ch - 1.0);
- c[0] = ellPar * ch * std::cos(pt[1]);
- c[1] = ellPar * sh * std::sin(pt[1]);
- return c;
- }
-
-
-
std::vector<Point<2>>
generate_shell_points(const Point<2> ¢er,
const double radius0,
const double radius1,
- const double ellPar)
+ const double eccentricity)
{
- const std::array<double, 2> radii{{radius0, radius1}};
+ const std::array<double, 2> radii{
+ {radius0 * eccentricity, radius1 * eccentricity}};
const std::array<double, 5> angle{
{0, numbers::PI_4, numbers::PI_2, 3.0 * numbers::PI_4, numbers::PI}};
std::vector<Point<2>> points;
+ // Create an elliptical manifold to use push_forward()
+ Tensor<1, 2> axis;
+ axis[0] = 1.0;
+ axis[1] = 0.0;
+ EllipticalManifold<2, 2> mani(center, axis, eccentricity);
for (auto &i : radii)
{
for (auto &j : angle)
{
- points.emplace_back(chart_to_cartesian(Point<2>(i, j), ellPar) +
- center);
+ points.emplace_back(mani.push_forward(Point<2>(i, j)) + center);
}
}
std::array<int, 6> dup{{1, 2, 3, 6, 7, 8}};
// center, and the major axis oriented in the direction of the x-axis.
//
// inner_radius and outer_radius parameters correspond to the
- // distances from the center of the manifold of the
- // crossing points of two concentric ellipsis with their major axis.
+ // semi-major axis length for the inner and outer ellipsis.
//
- // Input parameters must respect the following constrains:
- // c_parameter < inner_radius < outer_radius.
+ // Eccentricity must be in range ]0,1[
//
- // To understand the constrain on the c_parameter refer to the
- // documentation of function chart_to_cartesian() whithin this namespace.
void build_simple_hyper_shell(Triangulation<2, 2> &grid,
const Point<2> & center,
const double inner_radius,
const double outer_radius,
- const double c_param)
+ const double eccentricity)
{
unsigned int cell[][4] = {{5, 6, 0, 1},
{6, 7, 1, 2},
{15, 14, 12, 11},
{9, 15, 4, 12}};
std::vector<Point<2>> points =
- generate_shell_points(center, inner_radius, outer_radius, c_param);
+ generate_shell_points(center, inner_radius, outer_radius, eccentricity);
std::vector<CellData<2>> cells(8, CellData<2>());
for (int i = 0; i < 8; ++i)
for (int j = 0; j < 4; ++j)
Tensor<1, 2> axis;
axis[0] = 1.0;
axis[1] = 0.0;
- grid.set_manifold(0, EllipticalManifold<2, 2>(center, axis, c_param));
+ grid.set_manifold(0, EllipticalManifold<2, 2>(center, axis, eccentricity));
grid.set_all_manifold_ids(0);
}
void
test(unsigned int ref = 1)
{
- // deallog << "Testing dim " << dim << ", spacedim " << spacedim << std::endl;
-
Triangulation<dim, spacedim> tria;
switch (dim)
{
case 2:
- build_simple_hyper_shell(tria, Point<spacedim>(), 1.5, 1.8, 1.4);
+ build_simple_hyper_shell(tria, Point<spacedim>(), 1.0, 2.0, 0.8);
break;
default:
AssertThrow(0, ExcNotImplemented());
$NOD
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$ENDNOD
$ELM
512
projects / dealii.git / commitdiff
