Re: [Algorithms] It looks terrible (was: Lightmap Terrain)

[Klaus H. <k_h...@os...>]

Mark,

From: Mark Wilczynski <mwi...@cy...>
> Hi Niki,
>
> You could also try the trick that many people used when
> making outdoor levels for Quake based games.  They create a
> 2D grid of lightsources on a plane in the sky.  The
> brightness of each light is adjusted based on the sun
> position.  This method approximates an area light source
> (sky/clouds) instead of just a point light (sun).

This would be another option, but if I understand it correctly, then you
lose the properties of a directional light source. I'll have a look at the
modeling sites, though.

>  Search
> around the Quake modeling sites for more details.  By the
> way... I think your lightmap looks fine.  Lightmaps never
> look very good when viewed alone.

I disagree. I have tried the method I described, and the results look great
(including the dark sides of the mountains). The method has all the features
I was looking for, except that the shadows are still sharp (didn't take care
about this, yet). My current implementation of this is sort of brute force,
though:

I specify the position of the sun as a point on a unit sphere (longitude,
latitude). Then for each vertex of the surface, I calculate the vertex
normal, and then use this normal to calculate a second point on the unit
sphere (longitude, latitude). Then I compute the shortest distance between
the two points on the sphere (that is along the great circle). This gives a
distance in the range [0; PI]. I divide this distance by PI to get a
distance in the range [0; 1], and then I apply a bias-function to the
distance in order to compute the light intensity.

I'm sure there's cheaper methods to compute this, but here's some help for
those who'd like to try this:

float GreatCircleDistance(float lon1, float lat1, float lon2, float lat2)
{
    float theta = lon2 - lon1;
    float dist = acos(sin(lat2) * sin(lat1) + cos(lat1) * cos(lat2) *
cos(theta));
    if (dist < 0) dist += PI;
    return dist / PI;
}

A vertex normal can be converted into (lonVertex, latVertex) as follows
(y-component represents elevation):

lonVertex = atan2(normal.z, normal.x)
latVertex = atan2(normal.y, sqrt(normal.x^2 + normal.z^2))

For the shadow casting you may also need to convert the light source's
(lonLight, latLight) into a unit vector:

lightDir.x = cos(lonLight) * cos(latLight);
lightDir.y = sin(latLight);
lightDir.z = sin(lonLight) * cos(latLight);

The intensity is computed as follows:
I = GreatCircleDistance(lonLight, latLigh, lonVertex, latVertex);
I = 1.0f - pow(I, log(b) / log(0.5));

Where b is the bias. In this case, b is some value > 0.5 (I used 0.6). This
basically defines the gradient of the intensity over the sphere. I'll
probably try a couple of other functions, too, and see what yields the best
results.

> You have to blend them
> with a noisy base texture to get a decent effect.

The noisy base texture will further enhance the quality, yes.


Thanks,
Niki