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Just as XNA provided a useful function for creating projection matrices, so it provides another for orthographic projections two, in fact, as you will see. The first of these functions is the static Matrix.CreateOrthographic function. This expects the following four parameters: width: the number of units to display across the projection. The center point will always be 0, so providing a width of 4 will result in a frustum that extends from -2 to +2 across the x axis. height: the number of units to display vertically for the projection. Just as with the width, the center point will always be 0. zNearPlane: the near clipping plane distance. zFarPlane: the far clipping plane distance.

isOverShape() checks the camera position against all the visible shapes, with nearness based on the squared distance between each shape and the camera. Only the x- and z-axis values are considered, so it doesn t matter how high the camera is in the air.

ON condition of the outer join will filter the second data set in the outer join before the join is processed.

TIP Because distance has no effect on the sizing of objects, it is quite acceptable to set a near clipping plane with a negative distance, allowing objects that are effectively behind the camera to still be rendered. This configuration allows a coordinate system to be created where the value 0 is the center of all the 3D axes, which can simplify the object positional calculations.

The Cross Join (Cartesian Product)

TourCanvasGL.renderScene() draws the scene and also checks that the context is current, resizes the OpenGL viewport if necessary, and responds to the gameOver boolean being true: private void renderScene() { if (context.getCurrent() == null) { System.out.println("Current context is null"); System.exit(0); } if (isResized) { resizeView(); isResized = false; } // clear color and depth buffers gl.glClear(GL.GL_COLOR_BUFFER_BIT | GL.GL_DEPTH_BUFFER_BIT); gl.glMatrixMode(GL.GL_MODELVIEW); gl.glLoadIdentity(); glu.gluLookAt(xCamPos, yCamPos, zCamPos, xLookAt, yLookAt, zLookAt, 0,1,0); // position camera drawTree(); groundShapes.draw(gl); drawSphere(); drawFloor(); // execute display list for drawing the stars gl.glCallList(starsDList); // it calls drawStars(); if (gameOver) gameOverMessage(); } // end of renderScene() The game-specific parts of renderScene() are drawing the tree billboard, the ground shapes, the sphere, the floor, and the skybox, which are carried out by the highlighted draw methods and the display list.

Listing 7 21 shows an example orthographic projection matrix being created. Its vertical size is set at 16 units, and the horizontal size is calculated from the aspect ratio to display the appropriate amount to keep the coordinate system square. Listing 7 21. Calculating the normals for an indexed triangle list // Calculate the screen aspect ratio float aspectRatio = (float)GraphicsDevice.Viewport.Width / GraphicsDevice.Viewport.Height; // Create a projection matrix Matrix projection = Matrix.CreateOrthographic(16 * aspectRatio, 16, 0, 100.0f); Let s take a look at a couple of applications of orthographic projection.

A cross join, sometimes called a Cartesian product, unlike the other types of joins we ve covered so far, does not attempt to relate the two sets of data based on some key values Instead, it creates a result based on all possible row combinations in both sets of joined data Thus, the number of rows returned from a cross join is N M, where N is the number of rows in data set A and M is the number of rows in data set B Clearly, the number of rows in a cross join can quickly get out of hand! Most often, cross joins are done by mistake because the developer forgets to include an ON condition, which will force MySQL to use a cross join across the two data sets by default However, in some rare circumstances, the cross join can come in handy.