"Bald Eagle" <cre### [at] netscapenet> wrote:
> So here's how I got it to NOT crash, but my mapping results suck.
>
> Remove all of the protective select () and mod () functions, and it will crash.
>

Here's what you can do to make it work:

(Note that I might change my mind later about what values should
be used when the first expressions in the select statements
evaluates to zero. I may do some more testing in Python to be sure.)


> #version 3.8;

Replace with:

#version 3.7;  // I have not tested with v3.8


> #declare Zoom = 300;

Replace with:

#declare Zoom = 100;  // To see all the results


> #declare Image = pigment {image_map {"HyperbolicSoccerBall.jpg"} translate-0.5}

Replace with:

#declare Image =
    pigment {
        image_map { "HyperbolicSoccerBall.jpg" }
        scale <2, 2, 1>
        translate -<1, 1, 0>
    }
/*
To move the image from the region from x = 0 and y = 0 to
x = +1 and y = +1 into the region from x = -1 and y = -1 to
x = +1 and y = +1, as these are the intervals that the functions
below are made for.
*/


> #declare d2s = function (M, N, U, V) {
>  select (M,
>   select (2*(U*U + V*V - 2),
>    sgn (M) * sqrt (abs (-U*U -V*V + sqrt ((U*U + V*V)+(U*U + V*V + 4*U*U*V*V
> *(U*U+V*V-2)) )  / (2*(U*U + V*V - 2))) ) / M,
>    M,
>    sgn (M) * sqrt (abs (-U*U -V*V + sqrt ((U*U + V*V)+(U*U + V*V + 4*U*U*V*V
> *(U*U+V*V-2)) )  / (2*(U*U + V*V - 2))) ) / M
>   ),
>   M,
>   select (2*(U*U + V*V - 2),
>    sgn (M) * sqrt (abs (-U*U -V*V + sqrt ((U*U + V*V)+(U*U + V*V + 4*U*U*V*V
> *(U*U+V*V-2)) )  / (2*(U*U + V*V - 2))) ) / M,
>    M,
>    sgn (M) * sqrt (abs (-U*U -V*V + sqrt ((U*U + V*V)+(U*U + V*V + 4*U*U*V*V
> *(U*U+V*V-2)) )  / (2*(U*U + V*V - 2))) ) / M
>   )
>  )
> }

Replace with:

#declare d2s =
    function(U, V) {
        select(
            V,
            select(
                U*U + V*V - 2,
                sgn(U*V)*
                sqrt(
                    (
                        -U*U -V*V +
                        sqrt(
                            (U*U + V*V)*
                            (U*U + V*V + 4*U*U*V*V*(U*U + V*V - 2))
                        )
                    )/(2*(U*U + V*V - 2))
                )/V,
                U,
                sgn(U*V)*
                sqrt(
                    (
                        -U*U -V*V +
                        sqrt(
                            (U*U + V*V)*
                            (U*U + V*V + 4*U*U*V*V*(U*U + V*V - 2))
                        )
                    )/(2*(U*U + V*V - 2))
                )/V
            ),
            U,
            select(
                U*U + V*V - 2,
                sgn(U*V)*
                sqrt(
                    (
                        -U*U -V*V +
                        sqrt(
                            (U*U + V*V)*
                            (U*U + V*V + 4*U*U*V*V*(U*U + V*V - 2))
                        )
                    )/(2*(U*U + V*V - 2))
                )/V,
                U,
                sgn(U*V)*
                sqrt(
                    (
                        -U*U -V*V +
                        sqrt(
                            (U*U + V*V)*
                            (U*U + V*V + 4*U*U*V*V*(U*U + V*V - 2))
                        )
                    )/(2*(U*U + V*V - 2))
                )/V
            )
        )
    }
;
/*
Note that the plus symbols between the parentheses in the inner square roots
in your expressions are wrong; they should be multiplication symbols.
Also abs() should not be needed.
*/


> #declare s2d = function (M, N, X, Y) {
>  select (mod (M+FF, 1),
>   sqrt ((X*X + Y*Y - 2*X*X*Y*Y)/((X*X + Y*Y)*(1 - X*X*Y*Y))),
>   M,
>   sqrt ((X*X + Y*Y - 2*X*X*Y*Y)/((X*X + Y*Y)*(1 - X*X*Y*Y)))
>  )
> }

Replace with:

#declare s2d =
    function(X, Y) {
        select(
            X*X + Y*Y,
            select(
                1 - X*X*Y*Y,
                sqrt(
                    (X*X + Y*Y - 2*X*X*Y*Y)/
                     ((X*X + Y*Y)*(1 - X*X*Y*Y))
                )*X,
                sqrt(0.5)*X,
                sqrt(
                    (X*X + Y*Y - 2*X*X*Y*Y)/
                     ((X*X + Y*Y)*(1 - X*X*Y*Y))
                )*X
            )*X,
            0,
            select(
                1 - X*X*Y*Y,
                sqrt(
                    (X*X + Y*Y - 2*X*X*Y*Y)/
                     ((X*X + Y*Y)*(1 - X*X*Y*Y))
                )*X,
                sqrt(0.5)*X,
                sqrt(
                    (X*X + Y*Y - 2*X*X*Y*Y)/
                     ((X*X + Y*Y)*(1 - X*X*Y*Y))
                )*X
            )
        )
    }
;


> box {0, 1 translate -0.5 pigment {Image} translate -x}

Replace with:

box {
    -<1, 1, 0>, +<1, 1, 1>
    pigment { Image }
    translate +1.0*y
}


> //box {0, 1 translate -0.5 pigment {function {f_Image (s2d (x, y, x, y), s2d (y,
> x, x, y), z).red}} translate x}

Replace with:

box {
    -<1, 1, 0>,
    +<1, 1, 1>
    pigment {
        function {
            f_Image(
                s2d(x, y),
                s2d(y, x),
                0
            ).gray
        }
    }
    translate -2.5*x -1.0*y
}


> union {
>  #for (Y, 0, 1, Step)
>   #for (X, 0, 1, Step)
>    #declare C = f_Image (X, Y, 0).red;
>    #declare X2 = d2s (X, Y, X, Y)*Step;
>    #declare Y2 = d2s (Y, X, X, Y)*Step;
>    box {<X2, Y2, 0>, <X2+Step, Y2+Step, 1> pigment {rgb C}}
>   #end
>  #end
> }

Replace with:

union {
    #for (Y, -1, +1, Step)
        #for (X, -1, +1, Step)
            #declare C = f_Image(X, Y, 0).gray;
            #declare X2 = d2s(X, Y);
            #declare Y2 = d2s(Y, X);
            box {
                <X2, Y2, 0>, <X2 + Step, Y2 + Step, 1>
                pigment { color rgb C*<1, 1, 1> }
            }
        #end // for
    #end // for
    translate +2.5*x -1.0*y
}

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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