Fixing the Camera : help w math please

[patmurris]

I'm in the process of fixing up the WW camera so that it reports correct altitude and distance, and maybe doesnt go underground too often.

I managed to decipher most of the Camera.cs and WorldCamera.cs code and could fix up most of the faulty behavior... Bull is testing, and things work better so far.

However, i still dont understand the math used by the actual code to compute the camera distance from the target, knowing its altitude and the tilt angle.

Here is the camera logic as i understand it :



Here is the code i dont understand (from Camera.cs):

        protected void ComputeDistance( double altitude, Angle tilt )
        {
            double cos = Math.Cos(Math.PI-tilt.Radians);
            double x = _worldRadius*cos;
            double hyp = _worldRadius+altitude;
            double y = Math.Sqrt(_worldRadius*_worldRadius*cos*cos+hyp*hyp-_worldRadius*_worldRadius);
            double res = x-y;
            if(res<0)
                res = x+y;
            _distance = res;
        }

If anyone understand it, please point me in the right direction.

[patmurris]

Thats what i think it should be :

        protected void ComputeDistance(double altitude, Angle tilt)
        {
            double hyp = _worldRadius + altitude;
            double a = (_worldRadius + curCameraElevation) * Math.Sin(tilt.Radians);
            double b = Math.Sqrt(hyp * hyp - a * a);
            double c = (_worldRadius + curCameraElevation) * Math.Cos(tilt.Radians);
            _distance = b - c;
        }

Note : curCameraElevation is based on te * vertical exaggeration
(te = terrain elevation under the camera target)

[bull]

I asked Norman on irc to check this post, here is the reply

<+nhv> Bull I don't understand the problem distance is just EYE-TARGET where XYZ of EYE and TARGET LatLonElevation can be found by substituting appropriately for R http://mathworld.wolfram.com/SphericalCoordinates.html
<+nhv> R=EarthRadius + elevation

[patmurris]

I dont know the EYE (camera) position... i'm trying to compute it !!!
As i mentioned twice in my above post, i try to compute the distance only knowing tilt and altitude.

[nlneilson]

Originally Posted by patmurris

I dont know the EYE (camera) position... i'm trying to compute it !!!
As i mentioned twice in my above post, i try to compute the distance only knowing tilt and altitude.

EYE (camera) position is a known position from the drawargs.

The LatLon of the camera are known values.
this.drawArgs.WorldCamera.Latitude.Degre es,
this.drawArgs.WorldCamera.Longitude.Degr ees,

The altitude of the camera is also a known value but the WW code is a bit confusing, most of the civilized world uses altitude as distance above mean sea level while WW uses altitude as distance above terrain.
The value for hyp in your drawing would be:
this.drawArgs.WorldCamera.AltitudeAboveT errain
+
drawArgs.WorldCamera.TerrainElevation
+
the world radius

Note that WW uses the semi major axis of the earth ellipse (WGS84) for the world radius and calculation for a sphere, which is close enough for playing horseshoes but is no ringer.

The camera tilt is in one plane so the calculations can be done in 2D but if a person wants to us 3D calculations they can to make their head hurt. That can be done by hitting ones head against a hard object.

The exaggeration of the drawing may make the problem look harder than it is, the earth including the highest mountains to scale is smoother then a pool ball .

Without a trial an error type of iteration to see if the terrain (TARGET) is in the path of the center of the camera view I do not know how the distance from the camera to a point on the terrain, such as a mountain, can be done, it will be interesting to see what someone comes up with.

[withak]

Originally Posted by nlneilson

EYE (camera) position is a known position from the drawargs.

The LatLon of the camera are known values.
this.drawArgs.WorldCamera.Latitude.Degre es,
this.drawArgs.WorldCamera.Longitude.Degr ees,

Where do you think those numbers come from?

Of course all of those things are "known" from outside of the camera class, Patrick is fixing the calculations that go on inside of the camera.

[nlneilson]

Originally Posted by withak

Where do you think those numbers come from?

Will be interested to find where the Lat, Lon etc for the camera position comes from if it is different from where I think it comes from.

When WW starts the LatLon-etc is from WorldSettings.cs.
Any change of camera position is done "manually" by panning, zooming, by an html file, momentum or whatever. The only "calculation" for this is adding, subtracting or whatever to get the desired LatLon-etc for the camera.

From the LatLon-etc that is set/changed the graphics to be drawn and how it is to be drawn is calculated and displayed.

By stepping thru WW in debug this seems to be how it is done, after the LatLon-etc of the camera is "set" (in drawArgs) then the graphics are drawn accordingly.
Otherwise it would seem to be putting the cart before the horse.

The question from the original post is for the distance from the camera to a target. For a known and predictable surface such as a sphere or an ellipse this can be done directly. Where the terrain varies in elevation is the real problem, where is the intersection or target at the varying elevation.

The measure plugin, which I have not looked at the code yet, that draws a line on the surface or at the elevation of the terrain may give an indication of what/how this can be done.

[patmurris]

Forget about how to do it... i could sort it out from the first diagram and a new version of the camera code is being tested right now (#WW802 SVN Trunk).

My question was about understanding what the original code was computing... which doesnt fit the diagram. Just curious.

About the new camera code :

• Altitude is now the 'civilized world' camera elevation above sea level.
• Distance is to the camera target - on the globe surface (elevation zero) or at the terrain level depending on ElevateCameraLookAtPoint in the Options (default is terrain level).
• When colliding with the terrain, the camera will not 'bounce back' as before, but tilt back toward the vertical - and if not enough, it will put a bit more distance between the camera and the target, just enough to be above ground.

Also, a new camera setting option allows to go 'below sea level', but many things dont work anymore then. So this is still experimental, until WW can support negative altitudes for the camera.

Let me know if that works as advertised

[nigel_ht]

If you have the time could you add a mode so that we can change the camera to look in any direction? Like stand on the ground and look around, even up at the sky? DDH mentioned this would be simple to do but I never looked at the code.

When below sea level I guess we can turn off a lot of things that are broken (sky, etc).

Nigel