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view is facing. A game needs a score, so we ll track the number of moves the player has made, the objective being to solve the maze in as few moves as possible. The interface looks fairly simple, and that s because I want to spend most of the pages ahead concentrating on the 3D part of the game rather than on mundane control panel components. The 3D effect is quite an unusual use of the scene graph, and it demands careful forward thinking and node management. Let s start by looking at the theory behind how it works.
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10.1.1 Creating a faux 3D effect
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One evening, many years ago, I wandered up the road where I lived at the time, and found myself transported back to Victorian London. A most surreal moment! It happened that a film crew had spent the morning shooting scenes for an episode of Sherlock Holmes, and the nearby terrace housing had undergone a period makeover. If you ve ever visited a Hollywood-style back lot, you ll be familiar with how looks can deceive. Everything from the brick walls to the paved sidewalks is nothing more than lightweight fabrications, painted and distressed to make them look authentic. This may surprise some readers, but the walls in our project do not use any mindbending 3D geometry. The maze is nothing more than the illusion of 3D, creating the effect without any of the heavy lifting or number crunching. Now it s time to reveal its secrets. Picture five squares laid out side by side in a row. Now picture another row of squares, this time twice the size, overlaid and centered atop our original squares. And a third row, again twice as big (making them four times the size of the original row), and a fourth row (eight times the original size), all overlaid and centered onto the scene. If we joined the points from all these boxes, we might get a geometry like the one in figure 10.2. Figure 10.2 has been clipped so that some of the squares are incomplete or missing. We can see the smallest row of squares, five in all, across the middle of the figure. The next row has three larger squares, the extremes of which are partially clipped. There are three even larger squares, so big only one fits fully within the clipped area, with just a fragment of its companions showing. And the final row of squares is so large they all fall entirely Figure 10.2 The 3D in our maze is all fake. The outside the clipping area, but we can grid defines the maze geometry without using any complex mathematics. see evidence for them in the diagonal
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Amazing games: a retro 3D puzzle
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lines leading off at the far corners of the figure. This collection of squares is all we need to construct the illusion of three dimensions.
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10.1.2 Using 2D to create 3D
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So, the 3D effect in our maze is entirely constructed from a plain and simple 2D grid, but how does that actually work Figure 10.3 shows how the geometry of our 3D display is mapped to the 20 x 20 grid we re using to represent it. By using rows of squares and connecting their points, we can build a faux 3D view. The visible area exposed in figure 10.2 fits within a grid, 20 x 20 points. Using a grid of that size we can express the coordinates of every square using integer values only. Figure 10.3 shows how those points are distributed inside (and outside) the 20 x 20 grid. Remember: even though the diagram looks 3D, the beauty is we re still dealing with 2D x/y points.
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Our five smallest squares (let s say they re the farthest away) are each 4 points wide, with the first one having its top-left and bottom-right coordinates at (0,8)(4,12), the second at (4,8)-(8,12), and so on. The next row of three squares is 8 points in size: (-2,6)-(6,14), then (6,6)(14,14), and finally (14,6)-(22,14). The first and the last squares fall slightly outside the (0,0)-(20,20) viewport. The next row of three is 16 points in size: (-14,2)-(2,18), then (2,2)-(18,18), etc. The first and last squares fall predominantly outside the clipping viewport. The final row, not shown in figure 10.3, needs only one square, which falls entirely outside the clipped area, at (-6,-6)-(26,26).
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Figure 10.3 The geometry of our maze. Using a flat 20 x 20 grid as the viewport, the regular numbers describe x coordinates, and the rotated numbers (underlined) describe y coordinates.
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