Point-In-Triangle Test
Try out this little applet. Make sure you open the Java Console while you
run it so you can get additional feedback which will provide clues as to how
this applet works. In general, when you click inside the triangle, the
triangle changes color. When you click outside the triangle nothing happens.
But in the Java Console you get additional information to help you
understand the logic behind the visual presentation. You will also need to
study the code.
Here are the files for this applet:
Point2D.java
Tools2D.java
Triangle_click.java
The most interesting and most important of these files is the Tools2D.java
file:
<![CDATA[
class Tools2D{
static int area2(Point2D A, Point2D B, Point2D C){
int x = (A.x - C.x) * (B.y - C.y) - (A.y - C.y) * (B.x - C.x);
System.out.println("RESULT: "+x);
return x;
}
static boolean insideTriangle(Point2D A, Point2D B, Point2D C, Point2D P){
boolean inside =
Tools2D.area2(A, B, P) >= 0 &&
Tools2D.area2(B, C, P) >= 0 &&
Tools2D.area2(C, A, P) >=0;
System.out.println("---------------");
return inside;
}
}
]]>
The insideTriangle(Point2D,Point2D,Point2D,Point2D) method is called from
the Triangle_click class with the last point representing the coordinates of
a mouse click. If the mouse click is within the bounds of the triangle then
all three calls to Tools2D.area2 will return a positive value. The value of
each individual call gets displayed in the Java console. You should notice
that if a value is negative then no additional calls to Tools2D.area2 are
made.
The math behind why this works is a little complicated, but it has to do
with vectors and operations done with vectors. There is an alternative
trigonometric approach to solving this problem, but it's a little
complicated also. Just make sure you see how the logic of this applet works
and be ready to apply it to the assignment.
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ASSIGNMENT:
Inspect this applet and recreate it. You should
spend some time playing with it so you become aware of all the little things
it does. Make sure that you know what happens when the triangles are red,
white, and blue (in any order) or when all three are the same color.