POV-Ray

The SDL currently provides no way to compute the exact direction of a spline at a given location, even though mathematically this is a piece of cake: The first-order derivative of any spline section gives you the “speed” as a vector function, and is trivial to compute for polynomial splines (which are behind all spline types that POV-Ray supports); the normalized “speed” vector, in turn, gives the “pure” direction.

For exact direction/speed computations, I propose to extend the SDL invocation syntax as follows to allow for evaluating a spline’s derivative:

    SPLINE_INVOCATION:
        SPLINE_IDENTIFIER ( FLOAT [, SPLINE_TYPE] [, FLOAT] )

or

    SPLINE_INVOCATION:
        SPLINE_IDENTIFIER ( FLOAT [, FLOAT] [, SPLINE_TYPE] )

where the second FLOAT will specify the order of derivative to evaluate (defaulting to 0). In order to compute the position, direction, and acceleration of an object traveling along a certain spline, one could then for instance use:

    #declare S        = spline { ... }
    #declare Pos      = S(Time);
    #declare VSpeed   = S(Time,1);
    #declare VAccel   = S(Time,2);
    #declare Dir      = vnormalize(VSpeed);
    #declare Speed    = vlength(VSpeed);
    #declare AccelDir = vnormalize(VAccel);
    #declare GForce   = vlength(VAccel) / 9.81;

Alternatively, a mechanism may be devised to create a spline representing another spline’s derivative; however, it would be debatable whether the syntax should be parameter-like (being an added information that could be overridden again when creating other splines from such a derived spline), or operation-like (converting the spline), and in the latter case how it should affect spline type (and consequently control points); so the spline invocation parameter approach might be more straightforward, with less potential surprises for the user.

In version 3.7.0.RC7.msvc10.win64, there is a bug in rendering Bézier patches in which four points (along one edge) are all the same point.

The rendering can be seen here:
http://i.imgur.com/eq2UIXR.png [Edit: See attachment for the rendering]

As you can see, there is a visible unwanted artifact in the corner of each patch. The two patches shown are essentially the same, except with the 4×4 matrix of vertices transposed (just to demonstrate that simply transposing it didn’t fix it).

Expected rendering is a smooth surface without the artifact.

Below is the code used to render the above example.

#version 3.7;

global_settings { assumed_gamma 1.0 }

camera {

  location <45, 31, -10>
  look_at <40, 21, 200>
  right x*image_width/image_height

}

light_source {

  <660, 300, -525>
  color rgb 1

}

Example 1: First point in each row is the same point
bicubic_patch {
type 1 flatness 0.001
u_steps 4 v_steps 4
<32.2168, -23.78125, 0>, <34.4968, -23.78125, 0>, <35.2168, -23.78125, -0.72>, <35.2168, -23.78125, -3>,
<32.2168, -23.78125, 0>, <34.4968, -22.10256, 0>, <35.2168, -21.57244, -0.72>, <35.2168, -21.57244, -3>,
<32.2168, -23.78125, 0>, <33.9709, -21.55577, 0>, <34.52483, -20.85299, -0.72>, <34.52483, -20.85299, -3>,
<32.2168, -23.78125, 0>, <32.30556, -21.50298, 0>, <32.33359, -20.78352, -0.72>, <32.33359, -20.78352, -3>
rotate 180*x scale 1.4
translate ←5, 0, 0>
pigment { color <1, 0, 0> }
} Example 2: First row is all the same point
bicubic_patch {

  type 1 flatness 0.001
  u_steps 4 v_steps 4
  <32.2168, -23.78125, 0>, <32.2168, -23.78125, 0>, <32.2168, -23.78125, 0>, <32.2168, -23.78125, 0>,
  <34.4968, -23.78125, 0>, <34.4968, -22.10256, 0>, <33.9709, -21.55577, 0>, <32.30556, -21.50298, 0>,
  <35.2168, -23.78125, -0.72>, <35.2168, -21.57244, -0.72>, <34.52483, -20.85299, -0.72>, <32.33359, -20.78352, -0.72>,
  <35.2168, -23.78125, -3>, <35.2168, -21.57244, -3>, <34.52483, -20.85299, -3>, <32.33359, -20.78352, -3>
  rotate 180*x

  scale 1.4
  pigment { color <1, 1, 0> }

}

When rendering only a region of a file, using the command-line options +sc/+sr/+ec/+er, the area of the image that is excluded comes out as black in the final PNG.

Expected behaviour is for it to be transparent.