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CHAPTER 10 s GENERATING A TERRAIN
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Figure 10-12. A block in the terrain grid. If the X position inside the block is bigger than the Z position, the object is in the top triangle. Otherwise, the object is in the bottom triangle.
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After finding in which triangle the object is positioned, you can obtain the height of a position inside this triangle through a linear interpolation of the height of the triangle s vertices. Use the following code for the GetHeight method to calculate the height of a terrain s position:
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private float GetHeight(float positionX, float positionZ) { float height = -999999.0f; if (heightmap == null) return height; // Get the position relative to the terrain grid Vector2 positionInGrid = new Vector2( positionX - (StartPosition.X + Transformation.Translate.X), positionZ - (StartPosition.Y + Transformation.Translate.Z)); // Calculate the grid position Vector2 blockPosition = new Vector2( (int)(positionInGrid.X / blockScale), (int)(positionInGrid.Y / blockScale)); // Check if the object is inside the grid if (blockPosition.X >= 0 && blockPosition.X < (vertexCountX - 1) && blockPosition.Y >= 0 && blockPosition.Y < (vertexCountZ - 1)) { Vector2 blockOffset = new Vector2( blockPosition.X - (int)blockPosition.X, blockPosition.Y - (int)blockPosition.Y);
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// Get the height of the four vertices of the grid block int vertexIndex = (int)blockPosition.X + (int)blockPosition.Y * vertexCountX; float height1 = heightmap[vertexIndex + 1]; float height2 = heightmap[vertexIndex]; float height3 = heightmap[vertexIndex + vertexCountX + 1]; float height4 = heightmap[vertexIndex + vertexCountX]; // Top triangle float heightIncX, heightIncY; if (blockOffset.X > blockOffset.Y) { heightIncX = height1 - height2; heightIncY = height3 - height1; } // Bottom triangle else { heightIncX = height3 - height4; heightIncY = height4 - height2; } // Linear interpolation to find the height inside the triangle float lerpHeight = height2 + heightIncX * blockOffset.X + heightIncY * blockOffset.Y; height = lerpHeight * heightScale; } return height; }
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Notice that you use this method only to ensure that all scene objects are positioned over the terrain. To produce a realistic interaction between the objects and the terrain you would need to implement a physics system.
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To detect when an object in the scene intercepts a part of the terrain, you need to create some collision test methods. One useful collision test is between a ray and the terrain. For example, if an object is moving in the scene, you can trace a ray in the direction in which this object is moving and get the distance between it and the terrain.
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To check the ray and terrain collision, you ll do a collision test between the ray and the terrain s height map, instead of testing the ray against the terrain s mesh (many triangles). The collision test will be divided in two parts. In the first part, you ll do a linear search on the ray until you find a point outside (above) and another inside (below) the terrain. Then, you ll perform a binary search between these two points to find the exact collision point with the terrain. Figure 10-13 illustrates the linear search processes, where the nearest points outside and inside the terrain are found.
Figure 10-13. Linear search used to find one point inside and another outside the terrain
You can use the following code to perform the linear search on the terrain:
// A good ray step is half of the blockScale Vector3 rayStep = ray.Direction * blockScale * 0.5f; Vector3 rayStartPosition = ray.Position; // Linear search - Loop until find a point inside and outside the terrain Vector3 lastRayPosition = ray.Position; ray.Position += rayStep; float height = GetHeight(ray.Position); while (ray.Position.Y > height && height >= 0) { lastRayPosition = ray.Position; ray.Position += rayStep; height = GetHeight(ray.Position); }
After the linear search, the lastRayPosition variable stores the position outside the terrain and the ray variable stores the position inside the terrain. You then need to make a
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