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Just as with a perspective projection, we still have a near and far clip plane, and objects that are rendered will still be checked to ensure that they fall within this region. Despite objects not growing or shrinking as their depth changes within a scene, the depth buffer is still used and will ensure that objects with a higher z value will appear in front objects with a lower z value. The reason why depth has no effect on the object size is that objects at the far clip plane occupy exactly the same proportion of the plane as objects on the near clip plane. If you look back at Figure 7 2, you will see two objects, one near and one far, contained within a perspective viewing frustum, and then in Figure 7 3 the projected outcome on the screen of those two shapes. Let s repeat these with an orthographic viewing frustum. Figure 7 32 shows the objects within the frustum, one at the near clip plane and one at the far clip plane just as before.

Since the WHERE filter was executed after the two tables were joined, any rows without an ordered_on date equal to '2004-12-07' were removed from the returned resultset This eliminated any of the NULLed out rows for statuses having no matching orders, since NULL '2004-12-07' So, the question remains, how do we fulfill a request like this: Show all order statuses, and the number of orders in each status, for orders placed on December 7, 2004 The SQL in Listing 7-12 indeed filters the date properly, but, unfortunately, it also filters out all the nonmatching order statuses from the outer join To remedy the situation, we must use the ON clause to limit the compared data set of the right side of the outer join before the outer join occurs Listing 7-14 shows the correct SQL to fulfill the request Listing 7-14.

Figure 7 32. Two identically sized objects in the viewing frustum shown in 3D space When these objects are transformed by the orthographic projection, they continue to appear at the same size, as can be seen in Figure 7 33. The proportion of the clip plane filled by the shapes is the same in both cases, and so they are not enlarged or shrunk at all.

public int countVisibles(double xCamPos, double zCamPos) { if (numVisShapes == 0) // no shapes left return 0; int nearIdx = isOverShape(xCamPos, zCamPos); // is the camera near a shape if (nearIdx != -1) { visibles[nearIdx] = false; // make that shape invisible numVisShapes--; } return numVisShapes; } // end of countVisibles()

Corrected SQL Demonstrating the Outer Join ON Clause Filter mysql> SELECT osdescription, COUNT(coorder_id) AS "NumOrders" -> FROM OrderStatus os -> LEFT JOIN CustomerOrder co -> ON osorder_status_id = costatus -> AND coordered_on = '2004-12-07' -> GROUP BY osdescription; +-------------+-----------+ | description | NumOrders | +-------------+-----------+ | Cancelled | 0 | | Closed | 0 | | Completed | 1 | | In Progress | 0 | | Shipped | 0 | +-------------+-----------+ 5 rows in set (000 sec) If you are doing any sort of reporting work in MySQL, understanding this critical difference between seemingly similar SQL statements can help you avoid some very frustrating SQL debugging work Make sure you understand when to use a filter in the ON clause of an outer join and when to use a WHERE clause filter..

When we set up an orthographic projection, we simply tell it how many units we want it to use across the x and y axis. It will automatically stretch the rendered objects to fit within this defined set of coordinates. If the ratio of the axes does not match that of the screen, we can end up with objects becoming distorted as they are rendered. For example, if we used a range of -1 to +1 for both the x and y axes and displayed it on a 480 x 800 pixel screen, a 1-unit-square object would appear with a width of 240 pixels and a height of 400 pixels. It is clearly not square! For this reason, we generally still use the aspect ratio in our own calculations when setting the orthographic scale. There is no need for a viewing angle to be specified for this projection because the angle is always parallel.

private int isOverShape(double xCamPos, double zCamPos) // returns index of shape that the camera is 'near', or -1 { for(int i=0; i < NUM_SHAPES; i++) { if (visibles[i]) { double xDiff = xCamPos - (double) xCoords[i]; double zDiff = zCamPos - (double) zCoords[i]; if (((xDiff*xDiff) + (zDiff*zDiff)) < CLOSE_DIST) return i; } } return -1; } // end of isOverShape()

Remember that the WHERE clause will filter the results after the outer join is processed, whereas the Tip