OpenGL tile map morphing

I'm looking for a way to layout a tile map and change the heights of the vertexes.
Something like this (screenshot of some terrain in uo):


I found this, but I'm not sure if its the same thing as what I'm looking for (can't test the C++ code either - it seems to have been built for Mac ?)

Is there a special term for this type of rendering?
Any ideas?

Couldn't this be done with a standard 2d tile map? Sure it involves some clever "tile seams" between tiles, but I've seen even 8 bit nintendo games simulate height on a standard 2d tile map.

Wouldn't it be less taxing for tiles to share vertexes?

EDIT: I haven't a clue. In that case how would you transform the tile images to be displayed?

Kind of getting there..



I need to figure out the correct size translation for the map to have a 3d-look, isometric like.
I think the image as-is is at the correct angle..

SuperStrict

Framework brl.glmax2d
Import brl.pngloader

SetGraphicsDriver GLMax2DDriver()
Graphics 800,600,0

Global w:Float, h:Float
Global tex:Int = LoadTexture("tile.png")

glTexParameteri GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR
glTexParameteri GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR
glLoadIdentity
glEnable GL_TEXTURE_2D

Local mx:Float = 400, my:Float = 400
While Not KeyHit(KEY_ESCAPE)
	'mx = MouseX(); my = MouseY()
	
	Cls
	
	glLoadIdentity
	glBindTexture GL_TEXTURE_2D, tex
	glShadeModel(GL_SMOOTH)
	
	'Draw the texture
	glBegin GL_QUADS
	 glTexCoord2f 0.0, 0.0; glVertex2f mx, my - 50
	 glTexCoord2f 1.0, 0.0; glVertex2f mx + w, my
	 glTexCoord2f 1.0, 1.0; glVertex2f mx + w, my + h + 50
	 glTexCoord2f 0.0, 1.0; glVertex2f mx, my + h
	glEnd
	
	Flip
	
	Delay 10
Wend

End


Function LoadTexture:Int(url:Object)
  Local pm:TPixmap, id:Int
	
	pm = LoadPixmap(url)
	w = pm.width; h = pm.height / 2
	
	id = GLTexFromPixmap(pm)
	
	Return id
	
End Function