ingo <ing### [at] tagpovrayorg> wrote:
> How do I get the proper functions for defining a perspective camera as a
> user_defined one? There's all kind of stuff I can calculate, but can't
> get it into functions. Been at it for a few days, must say that young
> blokes playing games a meter away doesn't help either.
>
> I'd like to define location look at and angle, possibly roll.
> ...

Hi Ingo

The code below shows how you can transform the direction-functions for a user
defined camera.

--
Tor Olav
http://subcube.com

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

#version 3.8;

global_settings { assumed_gamma 1.0 }

#include "colors.inc"
#include "transforms.inc"

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

#declare pLocation = <0.0, 0.5, -6.0>;
#declare pLookAt = <0.0, 0.0, 1.0>;
#declare vDirection = pLookAt - pLocation;
#declare vRight = image_width/image_height*x;
#declare vUp = y;
#declare Angle = 90;

#declare vNewDirection = vDirection + 2.5*y;
#declare RotationAngle = 60;

#declare DirectionTransform =
    transform {
        Reorient_Trans(vDirection, vNewDirection)
        Axis_Rotate_Trans(vNewDirection, RotationAngle)
    }

#declare vT_X = vtransform(x, DirectionTransform);
#declare X_X = vT_X.x;
#declare X_Y = vT_X.y;
#declare X_Z = vT_X.z;

#declare vT_Y = vtransform(y, DirectionTransform);
#declare Y_X = vT_Y.x;
#declare Y_Y = vT_Y.y;
#declare Y_Z = vT_Y.z;

#declare vT_Z = vtransform(z, DirectionTransform);
#declare Z_X = vT_Z.x;
#declare Z_Y = vT_Z.y;
#declare Z_Z = vT_Z.z;

// To show where these components belong in a transformation matrix
//
// #declare vT_O = vtransform(<0, 0, 0>, DirectionTransform);
// #declare O_X = vT_O.x;
// #declare O_Y = vT_O.y;
// #declare O_Z = vT_O.z;
//
// #declare Transform =
//     transform {
//         matrix <
//             X_X, X_Y, X_Z,
//             Y_X, Y_Y, Y_Z,
//             Z_X, Z_Y, Z_Z,
//             O_X, O_Y, O_Z
//         >
//     }

#declare DX_Fn = function(u, v) { image_width*u };
#declare DY_Fn = function(u, v) { image_height*v };
#declare DZ_Fn = function(u, v) { image_width/2/tan(radians(Angle/2)) };

#declare NewDX_Fn =
    function(u, v) {
        0
        + X_X*DX_Fn(u, v)
        + Y_X*DY_Fn(u, v)
        + Z_X*DZ_Fn(u, v)
    }
#declare NewDY_Fn =
    function(u, v) {
        0
        + X_Y*DX_Fn(u, v)
        + Y_Y*DY_Fn(u, v)
        + Z_Y*DZ_Fn(u, v)
    }
#declare NewDZ_Fn =
    function(u, v) {
        0
        + X_Z*DX_Fn(u, v)
        + Y_Z*DY_Fn(u, v)
        + Z_Z*DZ_Fn(u, v)
}

#declare LocationX = pLocation.x;
#declare LocationY = pLocation.y;
#declare LocationZ = pLocation.z;

camera {
    user_defined
    location {
        function { LocationX }
        function { LocationY }
        function { LocationZ }
    }
    direction {
        function { NewDX_Fn(u, v) }
        function { NewDY_Fn(u, v) }
        function { NewDZ_Fn(u, v) }
    }
}

/*
camera {
    perspective
    location pLocation
    direction vtransform(vDirection, DirectionTransform)
    right vtransform(vRight, DirectionTransform)
    up vtransform(vUp, DirectionTransform)
    angle Angle
}
*/

/*
camera {
    user_defined
    location {
        function { LocationX }
        function { LocationY }
        function { LocationZ }
    }
    direction {
        function { DX_Fn(u, v) }
        function { DY_Fn(u, v) }
        function { DZ_Fn(u, v) }
    }
}
*/

/*
camera {
    perspective
    location pLocation
    direction vDirection
    right vRight
    up vUp
    angle Angle
}
*/

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

#declare Radius = 0.1;

sphere { < 0,  0,  2>, Radius pigment { checker White Black } }
sphere { < 0,  0, -2>, Radius pigment { checker White Red   } }
sphere { < 2,  0,  0>, Radius pigment { checker White Green } }
sphere { <-2,  0,  0>, Radius pigment { checker White Blue  } }

union {
    sphere { < 0,  0,  2>, Radius pigment { White } }
    sphere { < 0,  0, -2>, Radius pigment { Red   } }
    sphere { < 2,  0,  0>, Radius pigment { Green } }
    sphere { <-2,  0,  0>, Radius pigment { Blue  } }
    translate 0.5*y
}

background { color Gray20 }

light_source { <1, 1, -1>*100 White }
light_source { <0, 0, 0> Gray10 }

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

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