bool pointAboveLowerTriangle in Microsoft Word

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bool pointAboveLowerTriangle
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float finalHeight; if (pointAboveLowerTriangle ) { finalHeight = heightLxLz; finalHeight += zRelative * (heightLxHz - heightLxLz); finalHeight += xRelative * (heightHxLz - heightLxLz); } else { finalHeight = heightHxHz; finalHeight += (1.0f - zRelative) * (heightHxLz - heightHxHz); finalHeight += (1.0f - xRelative) * (heightLxHz - heightHxHz); } return finalHeight; }
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CHAPTER 5 GETTING THE MOST OUT OF VERTICES
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5-10. Calculate the Collision Point Between the Pointer and the Terrain: Surface Picking
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The Problem
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You want to find the exact 3D coordinates on your terrain at the position indicated by your pointer.
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As discussed in the introduction of recipe 4-19, the 2D point on your screen, indicated by your pointer, corresponds to a Ray in your 3D scene. In this recipe, you will walk over this Ray until you hit the terrain. You can do this using a binary search algorithm, which is capable of giving you the location of the collision with an accuracy of your choice. Given the hilliness of a terrain, it is possible that there are multiple collision points between the Ray and the terrain, as shown in Figure 5-20. Therefore, you will want to precede your binary search with a linear search so you make sure you detect the collision closest to the camera.
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This method converts the 2D screen position of the pointer into a 3D Ray. It is fully explained in the first part of recipe 4-19. private Ray GetPointerRay(Vector2 pointerPosition) { Vector3 nearScreenPoint = new Vector3(pointerPosition.X, pointerPosition.Y, 0); Vector3 farScreenPoint = new Vector3(pointerPosition.X, pointerPosition.Y, 1); Vector3 near3DWorldPoint = device.Viewport.Unproject(nearScreenPoint, moveCam.ProjectionMatrix, moveCam.ViewMatrix, Matrix.Identity); Vector3 far3DWorldPoint = device.Viewport.Unproject(farScreenPoint, moveCam.ProjectionMatrix, moveCam.ViewMatrix, Matrix.Identity); Vector3 pointerRayDirection = far3DWorldPoint - near3DWorldPoint; Ray pointerRay = new Ray(near3DWorldPoint, pointerRayDirection); return pointerRay; }
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Note In this version, you do not normalize the direction of the Ray. I ll explain this in a moment.
Now that you have this Ray, you re ready to detect collisions between the Ray and the terrain.
CHAPTER 5 GETTING THE MOST OUT OF VE RTICES
Binary Search
The Ray contains a starting point (in this case, where the Ray strikes the near clipping plane), as well as a direction. The Ray and terrain are shown in Figure 5-19. The starting point is indicated as point A. The direction of the Ray is the vector between point A and point B. The general idea behind the binary search is quite intuitive. You start with two points, A and B, of which you re sure that the collision point is located between them. Calculate the point between points A and B to find their midpoint, which is indicated by point 1 in Figure 5-19. You check whether this point is above or below the terrain. If this point is above the terrain (such as in the case of the image), you know the collision point is between point 1 and point B.
Figure 5-19. Binary search to detect a collision between Ray and the terrain You continue. Find point 2, between points 1 and B. This point is below the terrain, so you know the collision point is between point 1 and point 2. You continue to narrow down. Look at point 3, between point 1 and point 2. This point is again above the terrain, so the collision is between 3 and 2. Next, point 4 between 3 and 2 is below the terrain, so the collision is between 3 and 4. Finally, you check point 5, which is between points 3 and 4. You discover that the height of point 5 is very close to the height of the terrain at that (X,Z) position, so you have detected the collision point! Finding Point A and Point B In preparation for the binary search, you need to start with two points, A and B, on your Ray where you re sure the collision point is between them. You can safely use the starting position of your pointer Ray as point A, because it is the point on the Ray closest to the camera (it is positioned on the near clipping plane; see recipe 4-19). For now, you ll take the point where the pointer Ray strikes the far clipping plane as point B. This is not a bad choice, because it is the most distant point on the Ray that is still visible with your camera. As you can see in the GetPointerRay method explained in recipe 4-19, the pointerRay. Direction equals the vector you need to add to go from point A to point B. The Binary Search Method Now that you know point A and the direction to point B, you re ready to detect collisions with the terrain. The binary search algorithm explained earlier, translated into pseudocode, becomes this:
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