# Gradients on perspective projected Images..

• 03-24-2006, 10:39 AM
Nils Pipenbrinck
There's something I stumbled over while testing some gradients:

The gradients inherit the transform of the objects they are applied to. That makes perfect sense for me. In the spec this is only defined for the pathes, but ok - it makes sense to do the same for images as well.

However, the spec clearly states that paint transforms are affine only, and image transforms might be projective.

Now if I apply a gradient paint on a image drawn with perspective projection I don't know what results to expect. The reference implementation draws something, but it's hard to find out/guess how exactly the gradient should be drawn.

Question:

• Do we have to mimic the behaviour of the reference implementation for this special case? After all it's not defined in the spec.
[/*:m:xeh44fix]
• If so - how exactly should the gradient sampling work? Do we really have to sample the gradient projective?
[/*:m:xeh44fix]
• If we have to sample the gradient affine, how should we get rid of the projective transform?[/*:m:xeh44fix]

Hope someone can help me with these issues. After all - there's little to none traffic on this board..

Thanks,
Nils Pipenbrinck
• 03-24-2006, 11:00 AM
Nils Pipenbrinck
Here's a bit of code. draws a test image with radial gradient in perspective and affine mode.

Code :

```void Gradient_WTF (void) { VGfloat stops[10] = { 0, 0.8,0.2,0.1,1, 1, 0.1,0.2,0.8,1, };   VGfloat gradient[5] = { 128,128,128,128,60, };   VGfloat ImageMatrix[9] = { -0.4477, 0.8941, 0.0015, -0.8941, -0.4477, 0.0018, 370, 140, 1, };   // make checkerboard image: VGImage img = vgCreateImage (VG_sL_8, 256, 256, VG_IMAGE_QUALITY_BETTER); for (VGint y=0; y<256; y+=32) for (VGint x=0; x<256; x+=32) { VGfloat white[4] = { 1,1,1,1 }; VGfloat gray[4] = { 0.4,0.4,0.4,1 }; vgSetfv (VG_CLEAR_COLOR, 4, (x^y)&32 ? white:gray); vgClearImage (img, x,y,32,32); }   // make paint: VGPaint paint = vgCreatePaint(); vgSetPaint (paint, VG_FILL_PATH); vgSetParameteri (paint, VG_PAINT_TYPE, VG_PAINT_TYPE_RADIAL_GRADIENT); vgSetParameteri (paint, VG_PAINT_COLOR_RAMP_SPREAD_MODE, VG_COLOR_RAMP_SPREAD_REPEAT); vgSetParameterfv (paint, VG_PAINT_COLOR_RAMP_STOPS, 10, stops); vgSetParameterfv (paint, VG_PAINT_RADIAL_GRADIENT, 5, gradient);   // draw projective image: vgSeti (VG_IMAGE_MODE, VG_DRAW_IMAGE_MULTIPLY); vgSeti (VG_MATRIX_MODE, VG_MATRIX_IMAGE_USER_TO_SURFACE); vgLoadMatrix (ImageMatrix); vgDrawImage (img);   // draw affine image: vgLoadIdentity (); vgTranslate (400, 10); vgDrawImage (img);   vgDestroyImage (img); vgDestroyPaint (paint); }```
• 03-30-2006, 04:29 AM
Nils Pipenbrinck
anyone?
• 03-30-2006, 06:04 AM
Nils Pipenbrinck
Ok - if anyone is ever interested, this is what the reference implementation does:

Projective image matrices become unprojected before multiplication with the paint matrix. The unprojection works like this:

build 3 vectors that form a unit coordinate system in 2d:
vector v[3];
v[0] = vector(0,0);
v[1] = vector(1,0);
v[2] = vector(0,1);

transform these vectors by the image matrix (extend 2d vectors to homogenous 2d vectors by adding an implicit z=1). after transformation divide out the vectors x,y by z.

Then subtract projected origin from projected axis:

v[1] -= v[0];
v[2] -= v[0];

The output matrix directly built from these 3 vectors.

- translational part is equal to v[0],
- first column of upper 2x2 submatrix equals to v[1]
- second column of upper 2x2 submatrix equals to v[2]
- projective part becomes 0, 0, 1 (as usual for affine matrices)

I still scratch my head if this is fine with the standard.
• 03-30-2006, 09:12 AM
muratmat
Quote:

Originally Posted by Nils Pipenbrinck
...
I still scratch my head if this is fine with the standard.

OpenVG specifications do not clarify the correct behavior for perspective image matrixes coupled with a paint.
• 03-31-2006, 07:44 AM
Nils Pipenbrinck
Quote:

Originally Posted by muratmat
Quote:

Originally Posted by Nils Pipenbrinck
...
I still scratch my head if this is fine with the standard.

OpenVG specifications do not clarify the correct behavior for perspective image matrixes coupled with a paint.

Hm..

I doubt that this is intended.. For pattern images that wouldn't be such a big deal since it simplifies down to just a perspective image mapping, but the radial gradients are already hard enough to calculate.

Making them perspective correct would make almost all good optimizations impossible (e.g precomputed dda-method for scanlines).
• 03-31-2006, 09:19 AM
muratmat
Quote:

Originally Posted by Nils Pipenbrinck
Hm..

I doubt that this is intended.. For pattern images that wouldn't be such a big deal since it simplifies down to just a perspective image mapping, but the radial gradients are already hard enough to calculate.

Making them perspective correct would make almost all good optimizations impossible (e.g precomputed dda-method for scanlines).

I was talking about the correct behaviour that every user could expect, and that i think is the most correct one.
From an implementation point of view, it's normal to accept some compromises to not loose too much speed.
Anyway, i think that guys who wrote OpenVG specifications did not consider a such case, and that's why in my vector graphics framework (Amanith, do you know it?) i left gradient/pattern matrix independent from the "modelview" matrix.
• 12-13-2006, 09:26 AM
Espen
When there is a projective transform on an image, the image mode falls back to normal mode.