"Bald Eagle" <cre### [at] netscapenet> wrote:
> "Aj" <nomail@nomail> wrote:
> > Hello everyone,
> >
> > I created a spline object using the following code, but I could not get the
> > proper camera position. I was wondering if there is some systematic way to
> > figure out the camera position, and angle and look at vectors for a given shape.
>
> Yours might be easier, given that you have the grid locations on axes to guide
> you.
>
> Try imagining how the image you posted could be rotated in reverse to straighten
> the axes in the camera frustrum, and use those transforms on the object.
> The actual camera position might be a bit of trial and error to get exactly
> right.
>
> The look_at position might be obtained by extrapolating the x/z grid ticks and
> applying that inverse rotate transform.
>
> Maybe Francois LeCoat has a clever solution, as this seems right up his alley,
> or TOK has some words/code lines of wisdom to offer.

Hehe, there you tempted me to have a look at this.

I opened the screenshot in gimp and copied the 3 axes around to check if the
camera used could be a orthographic camera. It seems so.

See the attached image.

And here's some code ;-)

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
// Render options: +w640 +h480 +a0.3

#version 3.7;

global_settings { assumed_gamma 1.0 }

#include "colors.inc"

default {
    texture {
        pigment { color White }
        finish {
            diffuse 0
            emission color White
        }
    }
}

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

// Extreme values on the axes
#declare XN0 = -14.00; // *1e-3
#declare XP0 =  +4.00; // *1e-3
#declare YN0 =   0.00; // *1e-3 ?
#declare YP0 =  +1.00; // *1e-3 ?
#declare ZN0 =  -0.25; // *1e-3 ?
#declare ZP0 =  +0.05; // *1e-3 ?

// Divisions on the axes
#declare DivX0 = 2.00; // *1e-3
#declare DivY0 = 0.20; // *1e-3 ?
#declare DivZ0 = 0.05; // *1e-3 ?

// Number of divisions from the center of
// each axis to the axis endpoints
#declare XN1 =  -4.5;
#declare XP1 =  +4.5;
#declare YN1 =  -2.5;
#declare YP1 =  +2.5;
#declare ZN1 =  -3.0;
#declare ZP1 =  +3.0;

// These were found by trail and error
#declare ScaleX = 1.10;
#declare ScaleY = 0.96;
#declare ScaleZ = 1.64;

#declare FnX =
    function(x) {
        ScaleX*(XN1 + (x - XN0)/(XP0 - XN0)*(XP1 - XN1))
    }
;
#declare FnY =
    function(y) {
        ScaleY*(YN1 + (y - YN0)/(YP0 - YN0)*(YP1 - YN1))
    }
;
#declare FnZ =
    function(z) {
        ScaleZ*(ZN1 + (z - ZN0)/(ZP0 - ZN0)*(ZP1 - ZN1))
    }
;

#declare XN2 =  FnX(XN0);
#declare XP2 =  FnX(XP0);
#declare YN2 =  FnY(YN0);
#declare YP2 =  FnY(YP0);
#declare ZN2 =  FnZ(ZN0);
#declare ZP2 =  FnZ(ZP0);

#declare pNNN = <XN2, YN2, ZN2>;
#declare pPNN = <XP2, YN2, ZN2>;
#declare pPNP = <XP2, YN2, ZP2>;
#declare pNNP = <XN2, YN2, ZP2>;
#declare pNPN = <XN2, YP2, ZN2>;
#declare pPPN = <XP2, YP2, ZN2>;
#declare pPPP = <XP2, YP2, ZP2>;
#declare pNPP = <XN2, YP2, ZP2>;

#declare CylinderRadius = 0.02;

union {
    union {
        cylinder { pNNN, pPNN, CylinderRadius }
        cylinder { pNNP, pPNP, CylinderRadius }
        cylinder { pNPN, pPPN, CylinderRadius }
        cylinder { pNPP, pPPP, CylinderRadius }
        pigment { color Red }
    }
    union {
        cylinder { pNNN, pNPN, CylinderRadius }
        cylinder { pPNN, pPPN, CylinderRadius }
        cylinder { pPNP, pPPP, CylinderRadius }
        cylinder { pNNP, pNPP, CylinderRadius }
        pigment { color Green }
    }
    union {
        cylinder { pPNN, pPNP, CylinderRadius }
        cylinder { pNNN, pNNP, CylinderRadius }
        cylinder { pPPN, pPPP, CylinderRadius }
        cylinder { pNPN, pNPP, CylinderRadius }
        pigment { color Blue }
    }
}

#declare TickRadius = 2*CylinderRadius;

#declare TicksX =
    union {
        #for (X, XN0 + DivX0, XP0 - DivX0, DivX0)
            sphere { FnX(X)*x, TickRadius }
        #end // for
    }
#declare TicksY =
    union {
        #for (Y, YN0 + DivY0, YP0 - DivY0, DivY0)
            sphere { FnY(Y)*y, TickRadius }
        #end // for
    }
#declare TicksZ =
    union {
        #for (Z, ZN0 + DivZ0, ZP0 - DivZ0, DivZ0)
            sphere { FnZ(Z)*z, TickRadius }
        #end // for
    }

union {
    object {
        TicksX
        translate <0, YN2, ZN2>
    }
    object {
        TicksX
        translate <0, YP2, ZN2>
    }
    object {
        TicksX
        translate <0, YP2, ZP2>
    }
    object {
        TicksX
        translate <0, YN2, ZP2>
    }
    pigment { color White }
}

union {
    object {
        TicksY
        translate <XN2, 0, ZN2>
    }
    object {
        TicksY
        translate <XP2, 0, ZN2>
    }
    object {
        TicksY
        translate <XP2, 0, ZP2>
    }
    object {
        TicksY
        translate <XN2, 0, ZP2>
    }
    pigment { color White }
}

union {
    object {
        TicksZ
        translate <XN2, YN2, 0>
    }
    object {
        TicksZ
        translate <XP2, YN2, 0>
    }
    object {
        TicksZ
        translate <XP2, YP2, 0>
    }
    object {
        TicksZ
        translate <XN2, YP2, 0>
    }
    pigment { color White }
}

#declare SphereRadius = 2*TickRadius;
union {
    sphere { pNNN, SphereRadius }
    sphere { pPNN, SphereRadius }
    sphere { pPNP, SphereRadius }
    sphere { pNNP, SphereRadius }
    sphere { pNPN, SphereRadius }
    sphere { pPPN, SphereRadius }
    sphere { pPPP, SphereRadius }
    sphere { pNPP, SphereRadius }
    pigment { color White }
}

background { color Gray20 }

camera {
    orthographic
    location <-10.8, +4.9, -14.0>*0.6 // Found by trail and error
    look_at < 0,  0,  0>

}

// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7

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

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