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height in an isometric landscape

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Hello, I've recently started making a simple isometric game/simulation, and I've been stuck for a few weeks now trying to figure out what the neatest way was to implement the 'height' element of my terrain. So far, I just have tiles, and each tile has a height value. The problem is that I don't want it to be just blocks sticking out at a certain level, I want the landscape to flow. This means each tile (I'm using square tiles) has 4 corners, and I will have to determine the height of each corner by averaging out the 4 neighbouring heights:
| | |
| | |
(please forgive the bad ASCII art ;-)) anyway, if I would do this , it would create a nice quad for me that is skewed/stretched/etc to match the 4 corners.. the problem is, that my landscape is now not the level I had expected it to be, rendering the height value worthless (besides calculating these averages). Say I have a top of a mountain, where the heighest tile would be height 16, and all (eight) surrounding tiles would be 12. Using this system, each corner of the top tile would be (16 + 3*12)/4 = 13, so the mountain top would only be 13 high. The height value of the top tile would be useless for rendering objects/items/trees/etc on a certain height.. I've been considering a lot of options to solve this, but I won't bore you with all those now, or the thread will be too intimidatingly long to read for most people, and would only result in less feedback ;-) In short, what's a neat way to implement a flowing isometric landscape (think Settlers), without losing the height data? Thx in advance, Ko9 [Edited by - ko9 on July 28, 2006 1:43:10 PM]

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DarkBASIC uses a 3D matrix system in which you assign the heights of each corner, and it calculates polygons using lines between pairs of corners.

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Why do you need to average out the corners in the first place?

Isn't it simplier to do:

A ---- B
| |
| Tile |
| |
C----- D

And let Tile's height be interpolated by A through D?

If you're using 3D, don't average out heights at all
Drawing a quad based on dots A->D will suffice!


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Consider following picture:

1 step:
you need to find x,y coordinate of these vertices:
- 1,2,3,4,5
5.x = (A.x+B.x)/2;
5.y = (A.y+D.y)/2;

1.x = (A.x+5.x)/2;
1.y = (A.y+5.y)/2;

2.x = 5.x + (B.x+5.x)/2;
2.y = 1.y;

3.x = 1.x;
3.y = 5.y + (D.y+5.y)/2;

4.x = 2.x;
4.y = 3.y;

2nd step:
For calculating height of these vertices, you need to know height of tile plus height of surrounding tiles.

Height of tile is height of vertex no 5, so:
5.z = tile_height;

We need to calculate height of vertices ABCD:
A.z = (5.z+ T0.tile_height)/2;
B.z = (5.z+ T2.tile_height)/2;
C.z = (5.z+ T4.tile_height)/2;
D.z = (5.z+ T6.tile_height)/2;

Height of veretx 1 is 1.z = (5.z+ A.z)/2;
2.z = (5.z+ B.z)/2;
3.z = (5.z+ D.z)/2;
4.z = (5.z+ C.z)/2;

Here you can use greater slope and not use /2, but /3 or similar.
Also you must calculate z coordinates of vertices between A and B, B and C, C and D, and D and A.
AB.z = (5.z+ T1.tile_height)/2;
BC.z = (5.z+ T3.tile_height)/2;
CD.z = (5.z+ T5.tile_height)/2;
DA.z = (5.z+ T7.tile_height)/2;
3 step - drawing:
Because we are using 2D drawing there are no z coordinate. For achieving fake look of height just subtract height from y coordinate of vertex;
1.y -= 1.z;
2.y -= 2.z;

Another problem is shading them. You'll find that height is ok, but you need a light map for heights.

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