Start with the same framework code that you used to create the bouncing ball example in Chapter 1. You can use the same code from Chapter 1 that draws to an offscreen I ma g e in order to reduce flicker in the animation.
You can also borrow the code that draws a checkerboard background image, or you can invent your own creative background pattern. You also need to initialize a few variables in the applet's i n i t method to create a font for displaying the score and to handle a few other details for the preceding sections.
The F o n t M e t r i c s object f o n t Me t is called to compute the width of the string. The value f o n t H e i g h t is added to the y value of 1 o c so that the string is centered relative to the top center of the text. Game over If the game is over, you need to declare the winner. The following code displays the string "Win" beneath the winning player's score.
Figure Here's how the completed Ponglet game looks. Chapter 3 Hole In One. I6 Eius Chapter dating golf Making a click-and-drag putt interface Il g the physics of a ball erhaps you play golf as a personal pastime.
Or maybe you've putted a few holes of the miniature varietY down at the family fun center. If you have, you're in good company: Golf is a hugely popular sport in the United States, around the world, and even off the world. Golf has the distinction of being possibly the only game played on the surface of the moon, as Alan Shepard did on February 6, , during the Apollo XIV mission.
Reportedly, Shepard hit his first shot about yards and then badly shanked his second. Golf is also popular as a computer game. Dozens of versions of computer golf have appeared over the years. Some of these games present fanciful versions of the miniaturized game, some bear the names of famous players or golf courses, and some claim to be accurate simulations that model the physics and aerodynamics of real golf.
In this chapter, you won't be tackling anything as lofty as trying to calculate the wind forces on a golf ball in flight. Instead, this chapter's goal is to explore how to simplify the simulation of one aspect of golf, in this case putting, by faking the calculations just well enough to get a result that feels realistic.
By the end of the chapter you'll be ready to turn this knowledge into your own H o 1 e I n 0 n e applet. This chapter describes all the techniques used in the Ho1 e I n0ne applet. In truth, all calcula- avoiding needless complications.
Just a single take every single variable into account land blade of grass at the edge of the hole could even if you do, El Nino is just around the cor- prevent the ball from falling in. But do you ner. Some calculations just happen to be less really spoil the simulation if you treat the hole fake than others. Your goal should be to fake perhaps simplify Naah - it works just fine, as this chapter sounds better the calculations well enough to shows.
Modeling the Deceleration of a Ba!! Chapters 1 and 2 show code that simulates a ball that bounces around the screen and that moves at a constant speed. In the real world, balls behave differently. For example, a golf ball starts out moving at a certain speed proportional to how hard it's hit by the putter.
And immediately after the ball is hit, it starts to slow down as it travels toward the hole. This slow- down, or more formally, deceleration, is the result of a variety of forces acting on the ball, but deceleration of a golf ball is mostly caused by the rolling friction of the grass. When real objects decelerate or accelerate , Sir Isaac Newton's famous second law gets involved. Newton says that the deceleration of a real golf ball is proportional to the forces acting on it divided by the mass of the ball.
Simulated golf balls don't have real mass, of course, and they don't have real forces acting on them either, but you do need some type of calculation to simulate Sir Newton's law in action. The code in Chapters 1 and 2 moves the ball by adding values called dx and dy to the ball's x,y position.
Therefore, you've certainly deduced that slowing the motion of the ball is going to require you to reduce the dx and dy values. Before you start working out the details, though, you may want to consider vector math, a new way to do these types of motion calculations. You can slow the movement of your golf ball by reducing the distance it travels in each successive animation frame. However, the tricky part is reducing the distance the ball travels without changing the direction it's moving.
If you think of dx and dy as proportional to the length of two sides of a right triangle see Figure , the distance a ball travels when you add dx and dy is proportional to the length of the diagonal side of the same triangle. To compute the length of the diagonal you use the formula for the lengths of sides of right triangles, discovered by one Mr. Vector magnitude is important because it's the key to understanding how to decelerate your golf ball.
You can visualize what happens when you reduce the magnitude of a vector by examining the relationship between the three nested triangles in Figure However, notice that you subtract more from dx, than you do from dy,. If you were to subtract the same amount from dx, and dy e , you would change the shape of the triangle rather than just the length of the diagonal or more specifically, hypotenuse.
To keep the shape of the triangle the same, you need to maintain the same ratio between the lengths of the sides defined by dx and dy. The unit vector represents the direction the ball is moving, independent from the ball's speed. And because you divide dx and dy by the same number, you maintain the same ratio between dx and dy and therefore the same direction for the ball.
Chapter 3: Hole In One 35 When you divide a vector's dx and dy values by its magnitude, you get a new type of vector called a unit vector. The magnitude of a unit vector is always 1, hence the name. Unit vectors are used extensively in 2-D and 3-D graphics calculations because they can be used to represent a direction independent of speed.
You can also use a unit vector to calculate how to decelerate your ball without altering its direction. First, you calculate a unit vector from the ball's current motion vector. Then, because the magnitude of this unit vector is 1, you can scale it to any size you want by multiplying its dx and dy values by a value that represents the magnitude of the vector you want to create. Then, you simply subtract this vector from your original motion vector, and voila! Creating a vector class The golf simulation in this chapter uses vectors extensively to do many of the motion calculations, and you need code to perform the basic vector math operations, such as adding one vector to another, computing a unit vector, and so on.
So why not bundle up all these methods into a useful new utility class called V e c 2 D, like this: public class Vec2D I public float dx, dy; public void setVec float dx, float dy I this. For example, you can create a V e c 2 D object called v e 1 to control the motion of your golf ball. Then, after you have this V e c 2 D object, you can call the methods on it, such as s e t V e c to set the direction and speed of the ball by setting the d x and dy values in vel.
The methods addVec and subVec in V e c 2 D are used to add or subtract one vector from another. You use these methods in the Golf game to apply forces to the moving ball, such as the deceleration effect of friction and the force of gravity acting to push the ball into the hole whenever the ball crosses the edge of the rim.
The method u n i t V e c converts a vector into a unit vector. You can use this method in combination with m u 1 V e c to proportionally scale the d x and d y values in a vector by the f 1 o a t parameter passed to it by m u 1 V e c. Notice that u n i t V e c is coded to use the method m a g that returns the magnitude of the vector. With just these six vector operations, you can simulate all the motion dynamics needed to create a nice putting simulation.
So now that you have these code elements ready to go, move on to the next section where we present the code that uses these elements to simulate the golf ball and the hole on the putting green. Starting gain a Circle Your golf simulation requires code to simulate both a ball and a hole in the putting green. The code for simulating a hole shares many things in common with the code for a ball.
For example, to calculate when the ball rolls into the hole, you need code to compute the distance between the hole and the ball. So thinking along object-oriented lines, why not start by creating a common base class called C i r c 1 e to contain the code that is common to both a hole and a ball? Chapter 3: Hole In One 37 Creating the C i r c 1 e class Your C i r c 1 e class needs to define x, y, and d i a m values to store its location and size. It also needs to have a constructor to initialize these values.
And to simplify some of the calculations you need to do in your Ba 1 1 class, you need the constructor to initialize a value for the r a d i u s of the circle. Finally, you need code to compute the distance from one point to another; you can put this code into a method called d i s t.
You put code in B a 1 1 essentially to do the same thing as the bouncing ball in Chapter 1, but you can use your new V e c 2 D class see "Creating a vector class," earlier in this chapter to do the motion calculations.
The new features in Vec2D also help you handle decelerating the ball as it moves. The code for the Golf game uses v e 1 to hold the ball's d x and dy values and t v e c as a temporary variable to do your deceleration calcula- tions. You use the boolean flag s u n k to keep track of when the ball falls into the hole. In addition, you use s u n k in both B a 1 1 's d r a w method and in the code you write to implement the hole. Decelerating the ball The next job to tackle is the code to handle decelerating the ball.
You use this code in two different places, so you may as well put it into its own method called d e c e 1. Your dece1 code needs to start by checking that the magnitude of the ball's v e 1 vector isn't less than v a 1. If v e 1 is less than v a 1, the ball has slowed so much that if you were to further slow down the ball by subtract- ing the amount in v a 1 from v e 1, the ball would start to roll backward.
To avoid having the ball roll backward, you can simply set the vel vector to zero. It initializes by calling s e t V e c and passing v e 1 's d x and dy values, which gives you a copy of v e 1 in t v e c. Next, you call the u n i t V e c method to convert t v e c into a unit vector.
Then you call muI Vec to shrink this vector down to the same magnitude as v a 1. Finally, you subtract this scaled vector from v e 1 by calling subVec. The code for the Golf game uses vel to hold the ball's dx and dy values and tvec as a temporary variable to do your deceleration calcula- tions.
In addition, you use s u n k i n both B a 1 1 's d r a w method and in the code you write to implement the hole. Your decel code needs to start by checking that the magnitude of the ball's v e 1 vector isn't less than v a 1. To avoid having the ball roll backward, you can simply set the ve 1 vector to zero.
It initializes by calling s e t V e c and passing v e 1 's d x and dy values, which gives you a copy of vel in tvec. Then you call mu 1 Vec to shrink this vector down to the same magnitude as v al.
Chapter 3: Hole In One 39 Moving the ba« Now that you've conquered deceleration, you can write the code to imple- ment B a 1 1 's m o v e method. This method is the one your applet calls to advance the ball's position on each frame of the animation.
Your move method takes two parameters: The first parameter, bd , specifies the bounds of the applet. You need bd to detect when the ball needs to bounce off the edges of the applet so that it doesn't roll out of the applet's play field.
The second parameter, f r i c t i o n , specifies how much to decelerate the ball for each frame of animation. You use f r i c t i o n to call d e c e 1 in order to update the ball's deceleration, like this: Calling d e c e 1 updates v e 1 to account for deceleration, after which you can add v e 1 to the ball's position to move the ball. You need to modify the ball's position in one other place in your code, so you may as well create a method in B a 1 1 for this purpose: You can call it a d d P o s.
Sf ; You use the boolean flag hi tEdge to signal that the ball has bounced off a vertical or horizontal edge. Then, you use the d e c e 1 method to reduce the ball's speed by 80 percent after a rebound by multiplying v e I's current magnitude by. Putting the bait You also need to add code to Bal 1 to support a mouse-driven, click-and- drag putt interface.
Using this interface, the player can click on the ball to select it. Then, while holding down the mouse button, the player can drag the mouse cursor back in the direction opposite from the hole, as shown in Figure Doing so draws a rubber-band line from the mouse's current position to the ball. The player can then use this line to aim a putt. The player makes the putt by releasing the mouse button. The length of the rubber-band line when the button is released indicates the force of the putt- Figure The golf game i nterface uses a i rubber- band style display to control the direction!
I and force of a putt. First, you need a method called t o u c h e s to detect when the user clicks the ball: public boolean touches int mx, int my t return new Circle mx, my, 0. You use these values to create a new C i r c 1 e object located in the spot where the user clicked.
Then you can call C i r c l e's d i s t method to calculate the distance from this point to the center of the ball. If this distance is less than the ball's r a d i u s, t o u c h e s returns true, indicating that the user has clicked the ball.
Creating a Po i nt object in this example, pt r is a convenient way to pass x,y values as a single parameter. Using these values, p u t t calls s e t V e c to set the ball's v e 1 variable in order to put the ball in motion. Here's the code for putt : public void putt Point ptr I vel. Dividing by 20 provides greater resolution for aiming the putt without imparting too much force to the ball. However, you can adjust this value to suit your own preferences.
Waiting for the ball to go in You need a final method to support the putting interface: moving. The Golf applet calls moving in order to check the d x and dy values in v e 1 and returns t r u e if the ball is currently in motion. Your interface code can use this method to prevent the player from trying to select the ball while it is still in motion from the last shot.
To add a nice 3-D effect, you can code d r a w to put a shadow beneath the ball. You can create a shadow by drawing a dark gray circle offset two pixels down and to the right of the ball. If you tie a rock to a string and whirl it around Why invent a fictitious force? Well, sometimes your head you can demonstrate centrifugal simulating a fictitious force is easier than com- force. However, centrifugal force isn't really a puting all the effects of real forces - such is force at all.
You are merely seeing the result of the case for your golf simulation. There isn't a the ball's inertia as it orbits around your head.
This type of pretend force is called, appropri- ately, a fictitious force. The shadow needs to be drawn before the ball; however, you don't want a shadow when the ball is in the hole. You can check the state of the s u n k flag to see whether the ball is in the hole, and if so, not draw the shadow.
Also, when the ball is in the hole, it looks better to draw it in light gray in order to simulate the darkness of looking down into a real golf hole. Here's the code for draw : public void draw Graphics g i f! H o 1 e is a little trickier to create than Ba 1 1 because the physics of how a real golf ball interacts with a real hole are far from simple.
However, by using your new V e c 2 D code and by faking the calculations, you can get nice results without too much work. Inside H o 1 e you can write a constructor that sets the position and size of the hole. H o 1 e also requires a temporary vector for its calculations, so you can go ahead and declare a V e c 2 D object called t v e c for this purpose. However, when the ball strays close enough to the edge of the hole, gravity, using the hole as a lever, tries to push the ball into the hole.
If the ball is moving fast enough and is at a sufficient distance from the hole's center, the ball escapes the force pulling it in. If not, gravity wins, and the ball is captured, spinning around futilely at the bottom of the hole until it slows to a stop. The force of gravity normally can only push a ball down against the grass.
However, when the center of gravity of the ball is inside the radius of the hole, the force of gravity gets redirected by the lip of the hole and creates a fictitious force that seems to push the ball toward the center of the hole. In your simulated golf game, this happens whenever the distance from the center of the ball to the center of the hole is less than the radius of the hole, as shown in Figure If you were to more closely simulate the forces acting on the ball, you'd have to consider that the fictitious force acting on the ball changes as the ball moves closer toward the center of the hole.
This happens because the edge acts like a ramp that gets steeper and steeper as the ball topples into it. You could add code to simulate this, but you don't need to be this precise in order to get a realistic result.
The important part is that the ball reacts as if a force is pushing it toward the center of the hole. Vectoring in When you animate the ball by adding the v e 1 vector to the ball's position, you use v e 1 to simulate the force of the putter acting on the ball and the ball's resulting momentum pushing it in a particular direction. The fictitious force pushing the ball to the center of the hole can also be represented by a vector. However, the effect of the hole doesn't replace v e 1 's effect on the ball.
Instead, the hole's effect gets added to v e 1 and changes the direction of the force created by the ball's momentum. You can simulate the effect of combining two different forces by adding the vectors that represent those two forces.
And, as Figure shows, when you add two vectors, you get a new vector that represents their combined forces. The new vector can have a greater magnitude than the two vectors you add, or it can produce a vector that has an equal or lesser magnitude, depending on the values of the two vectors you add.
Curving around the hole In the case of a fast moving ball that only grazes the edge of the hole, the fictitious force acting to push the ball into the hole is much weaker than the force of the ball's momentum.
So the combined force only manages to de- flect the ball's path. However, because the fictitious force deflects the ball in the direction of the hole's center, the force keeps on pushing on the ball as long as it stays near the hole. And this curved path may even move the ball closer to the center of the hole and wind up causing the ball to spiral in.
If not, the ball's path eventually leads away from the hole, and the ball travels off in a new direction. Ball's 1nom"nlt! Part I: Steppin' Out Coding the curve Now that you've got the theory down, you're ready to start converting it into real code. You can start by adding a method to H o 1 e called i n f 1 u e n c e in which you put the code that computes the fictitious force acting to push the ball into the hole. You also need to put code in i n f I u e n c e to detect when the ball has been captured by the hole, and in turn set the s u n k flag to t r u e.
Also, although not strictly necessary, it's fun to add code that simulates the effect of a sunk ball bouncing around in the hole until it settles to a stop. Your i n f 1 u e n c e code starts by computing two values to which you need to refer in several places in the code.
The second value, h b D i s t , must be set to the distance from the center of the ball to the center of the hole; you can determine this distance by calling the C i r c I e method d i s t. These values are used to determine if the ball has strayed close enough to the hole that the fictitious force should begin acting on it.
If the h b D i s t is less than the r a d i u s of the hole and greater than d i s t I n , then the fictitious force should act on the ball. If h b D i s t is greater than the radius of the hole, then the ball's center of gravity is not inside the diameter of the hole, and the fictitious force has no effect on the ball.
If h b D i s t is less than d i s t I n , then the ball has fallen completely into the hole and is no longer in contact with the lip of the hole, so the fictitious force should stop acting on the ball.
Pushing to the center Whenever the fictitious force is acting on the ball, you can simulate its effect by computing a unit vector that points from the ball's center to the center of the hole. So you can use a d d V e c to add this new vector to the ball's momen- tum vector v e 1 , like this: ball. At its heart, this check looks to see whether the distance from the ball's center to the hole's center h b D i s t is less than the radius of the hole minus the radius of the ball d i s t I n.
But for a little extra realism, you want to first make sure that the ball isn't moving too fast to simply skip over the hole. Skipping over is what a real ball does, even if it is hit to the dead center of the hole. You can check for a reasonable speed by comparing the magnitude of v e 1 to the hole's radius. This comparison isn't a precise calculation, but it works reasonably well.
The result of these checks set the ball's s u n k flag, like this: ball. Spinning in the hole Even after the ball drops into the hole, the ball's momentum vector still tries to make it move. A real golf ball bounces off the sides of the hole, but your Hol e class doesn't yet include any code to simulate this. So unless you add more code, the Java golf ball would simply keep moving as if the hole weren't there.
The way you can simulate a ball bouncing off the inside of a circular hole is similar to the approach you use in the section "Staying in bounds" in order to make the ball bounce off the edges of applet's display area see Chapter 1.
In effect, you wait until the ball has moved outside the bounds of the hole and then compute a new location and path for the ball that mimics the path the ball would have taken if it had bounced off the sides of a real hole. The first step tests whether the ball has been sunk. If it has, the code needs to check whether the ball has moved beyond the bounds of the hole: ball. You also need to calculate the new direction the ball will be moving after this bounce and change the ball's v e 1 vector to make the ball move in that new direction.
The calculations to do this so that the movement is modeled on the real-life behavior of a ball can get quite complex. However, because this effect is only for show, you can just fake it. A real ball bounces off the sides of a hole on a path that is related to the angle between the point where the ball touches the side of the hole and a radial line between the center of the hole and this point.
However, just calculating the point of intersection requires more math than you need to use here. Instead, you can simply compute a vector to apply a force to the ball that pushes it back toward the center of the hole by an amount proportional to the distance the ball has strayed outside the hole.
Here's the code: tvec. Again, you can resort to sheer fakery by simply moving the ball back toward the center of the hole by an amount proportional to how far the ball moved beyond the bounds of the hole. You mostly need to fill in the details that follow from the work you've already done in Chapters 1 and 2. For example, you need to create a run method and Th read to handle the animation. The complete code is on the CD-ROM included with this book, so you can look there if you've forgotten any details.
Completing the putting interface You still need to add the applet side of the code in order to complete the rubber-band putting interface.
As discussed in the earlier section "Putting the ball," your code must use a Poi nt object to record the position of the mouse and pass it to the p u t t method in B a 1 1. And you need to override the applet methods mouseDown , mo useDrag , and mo useUp to imple- ment the full mouse interface. Chapter 4 JavaPool It also appeals to physicists because it demonstrates, in a fun way, some of the basic laws that make the universe work. For example, when a billiard ball smacks, dead center, into another billiard ball, the moving ball comes to a complete stop.
The second ball steals the first ball's momentum and travels off at nearly the same velocity as the first ball - basic physics demonstrated with elegant simplicity. This chapter shows you how to create a simplified game of billiards in Java. However, the main point of this chapter is to introduce you to the art and science of collision detection. Because of the math involved, programmers often regard collision detection as one of the more difficult problems lurking i n game design. However, the goal of this chapter is to get you past the math and down to useful techniques that you can use to get results.
This chapter also shows you how to simulate the physical laws that control how one billiard ball bounces off another. Simulating billiards and program- ming collision detection requires a bit of math, but don't panic; the math isn't that hard to use, even if you don't understand all the physics behind it.
In the end, all equations turn back into Java code so that only your com- puter has to worry about them. This chapter largely deals with the concepts you need to understand to write code that can detect and handle collisions.
However, simulating the interaction of billiard balls is a little more complicated because billiard balls bounce off each other, not just static boundaries or holes. This is tricky to simulate because you have to compute both the exact moment when two balls collide and the exact point at which they touch in order to simulate properly the rebound from the collision.
Passing in the night Before you think too much about billiard balls, start by imagining two ocean liners sailing across the sea.
One liner is heading in a northeast direction and the other is heading in a southeast direction. If both ships are the same distance from this intersection crossing point and if both ships are traveling at the same speed, it's obvious that the two ships arrive at the intersecting point at exactly the same time.
In other words, the ships are on a collision course man the lifeboats. If one ship is just a ship's length closer or farther from the point of intersec- tion, the two ships won't collide.
Instead, the closer ship passes the inter- section point, just as the other ship arrives at it. The passengers scream, but the ships don't collide. Likewise, if one ship travels sufficiently slower or faster than the other, the two ships don't collide because the faster ship clears the intersection point before the slower ship arrives. In between the possibility of one ship passing the intersection point before the other arrives and a full on collision, is a tiny window of time where the slower or more distant ship reaches the intersection point before the other ship completely passes it.
Exactly when the slower or more distant ship arrives determines where it hits the other ship. If it arrives at nearly the same time as the other ship arrives, it rams into the front of the other ship.
If the slower, or more distant ship arrives just slightly before the other ship passes the intersection point, it clips the rear of the other ship. Reducing the distance As the two ships approach the point where their paths cross, the distance between the two ships gets smaller and smaller. All this decreasing and increasing of distance means that there must be a point in time at which the distance between the ships is as small as it's going to get.
If this distance is small enough, both ships will try to sail into the same place at the same time and means that the ships are doomed to collide. However, if this distance is large enough, both ships can pass without a collision. In between these two distances, you need to know the shape and size of each ship in order to calculate how close the ships can pass before risking a collision.
You see the obvious parallel between ships on an ocean and billiard balls on a pool table, of course. However, unlike ships, billiard balls are spheres of the same size, and calculating how close two billiard balls can get to each other without colliding is much easier than a ship shape. Because real billiard balls are never exact spheres, this distance, measured from the center of one ball to the center of the other, is just a hair larger than twice the radius of a billiard ball.
However, for your pool simulation you can simplify this to simply twice the radius. Calculating position over time I magine a billiard ball rolling across the felt surface of a real pool table at a constant speed.
Then, imagine a ruler lying on the table parallel to the path of the billiard ball, as shown in Figure At time zero, the ball is at position 1 on the diagram, and the ball is moving at a speed that carries it to position 4 one second later. In other words, the distance the ball travels is proportional to time. If you know the position of the ball at any two points and you also know the time it takes for the ball to travel between those two points, you can calcu- late the position of the ball at any point in time.
In one full second, the x value increases by 8 4 x 2 and the y value decreases by 12 4 x 3. When you animate a moving ball, you add dx and dy to the ball's x and y position values at each tick of the animation. You may recall that the distance between two points pointl and point2 is the square root of point Lx - point2.
This formula is called the distance formula. Now that you know how to calculate the position of a moving ball over time, you can use this formula to compute the distance between two moving balls, bl and b2, over time.
Chapter 4: JavaPool 55 Ball bl's current position is given by bl. For each animation tick, ball bl adds bl. Likewise, ball b2 adds bl.
It's a rather large formula, but it's really just an expanded form of the distance formula listed at the start of this section. The difference is that the expression bl. Using this formula, you can take any two moving balls and calculate the distance between them at any future point in time. For example, you can use this formula to see whether two balls collide in the next tick of the anima- tion clock by computing the distance and checking whether it is less than twice the radius of the balls.
However, using the formula in this fashion isn't a foolproof solution. For example, Figure shows the paths of two moving balls. As Figure shows, the two balls should have collided at the position shown by the dotted outlines. However, the code can fail to detect this if it only checks for collisions at fixed time intervals. You can try to solve this "missed collision" problem by using a loop to check the distance between the two balls at points in time even closer together than a single animation tick.
However, unless you were to loop until you were checking extremely tiny distances, computing the exact time one ball its another would be difficult. You need to know the exact time to calculate the exact location of each ball when the collision happens.
If you don't know the exact position of both balls at the moment of collision, you can't prop- erly calculate the result of the collision. Even a small error in position can make a big difference in the direction and speed of the balls after the Lision. Solving for time If you still remember any high-school algebra, you probably recall that formulas - like the one presented in the previous section for computing distance over time - can be rearranged to solve for specific values.
From the position, direction, and velocity information for two objects at a speci- fied time, the distance-over-time formula calculates the distance separating the two objects. You already know that the only distance you care about is the distance at which two balls collide, which is twice a ball's radius.
Two solutions? Although your algebra may be a bit too rusty to figure out how to solve the distance-over-time equation for time, some quite sophisticated computer programs are available that can do it for you. One such program, Mathematica 3. With the solved equation, you can spend time working on your code rather than digging through your old math textbooks. As the balls approach the intersection point, the distance between the balls becomes equal to radius x 2 at the point marked Solution 1.
However, as Figure 43 shows, at another place on the path marked as Solution 2, the distance between the balls is also equal to radius x 2.
Physically, only Solution 1 makes any sense because the balls collide at that point and can never reach the position for Solution 2 unless they pass through one an- other. It will also give you an understanding of texture mapping and advanced imaging techniques. It focuses on the application and uses examples to bring the highly technical topic alive for students, making it easier for them to absorb the information.
This comprehensive guide will give you a number of reusable techniques, to create awesome action-packed games. CodeGym University. Light theme. Articles All groups. Published in the Random group.
Java is widely used by indie game development companies and for creating mobile games. The Ins and Outs of Java Game Programming for Beginners Java is easy-to-use, so a beginner can learn to create a range of programs and write reusable code, easily moving between computer systems as they do so. The more experienced you are, the higher your position will be, hence your salary will grow. We have outlined a Java game development for dummies learning plan to help you on your way.
It has a tutorial that walks you through creating your first Android app. If you already know Java Core, it would be helpful to learn about game components, such as GUI graphic user interface , game graphics and physics, and sound. It has sufficient documentation to get you started. What else? Every professional should know it and GitHub, the largest web service for hosting IT projects and their joint development.
Some Indie developers make all the game from scratch, with all graphics, design level maps, textures, sprites of characters, texture atlases, but for your first projects you may use free graphics from different resources.
Once you get the hang of Android app development, you can start practicing on making games. The Internet is full of written and video tutorials on making simple games. Technologies progress, users, shift interests and become more demanding, so you need to constantly improve your skills. Just remember to divide your time between researching topics and doing practical exercises, spend more time on practice. Skip to content. Sign in Sign up. Instantly share code, notes, and snippets.
Created Aug 28, Code Revisions 2 Stars 9 Forks 7. Embed What would you like to do? Embed Embed this gist in your website.
Share Copy sharable link for this gist. Learn more about clone URLs. Download ZIP. Almost 1, "For Dummies" eBooks that I have.
All of the eBooks. This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
0コメント