Class E_point

An instance of this class represents a point on the embedded surface EX(a)

This is the value of $a$, where we are considering $EX(a)$.

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

This is computed from a by the set_a() method

Coordinates of the point

A unit vector orthogonal to $x$, $n$ and $v$

A unit vector orthogonal to $x$, $n$ and $u$

Normalised gradient of $g$

Basic G-invariant functions of $x$

Norm of the gradient of $g$

Square norm of the gradient of $g$

Inverse norm of the gradient of $g$

Gaussian curvature of the surface

This method adjusts the coordinates of a point to ensure that it lies on the surface $EX(a)$ and in the fundamental domain. Moreover, if the constraint field is set to a value indicating that the point should lie on one of the curves $C_0$, $C_1$, $C_3$ or $C_5$, then the coordinates are adjusted if necessary to ensure that that holds.

This method sets this["n"] to the normalisation of the gradient of $g$ at the point this["x"]. It uses the simp() function, which simplifies symbolically unless we have any floating point subexpressions, in which case it evaluates numerically.

This method sets this["u"] and this["v"] in such a way that [this["x"],this["n"],this["u"],this["v"]] is an oriented orthonormal basis for $\mathbb{R}^4$.

This method sets the current point to lie on the curve $C_0$. As the parameter $t$ runs from $0$ to $1$, the point covers the section of $C_0$ contained in the fundamental domain $F_{16}$ starting with $v_6$ at $t=0$, and moving to $v_3$ at $t=1$.

This method sets the current point to lie on the curve $C_1$. As the parameter $t$ runs from $0$ to $1$, the point covers the section of $C_1$ contained in the fundamental domain $F_{16}$ starting with $v_0$ at $t=0$, and moving to $v_6$ at $t=1$.

This method sets the current point to lie on the curve $C_3$. As the parameter $t$ runs from $0$ to $1$, the point covers the section of $C_3$ contained in the fundamental domain $F_{16}$ starting with $v_{11}$ at $t=0$, and moving to $v_3$ at $t=1$.

This method sets the current point to lie on the curve $C_5$. As the parameter $t$ runs from $0$ to $1$, the point covers the section of $C_5$ contained in the fundamental domain $F_{16}$ starting with $v_0$ at $t=0$, and moving to $v_{11}$ at $t=1$.

This sets the current point to a randomly generated point in $F_{16}$