Basically what I want to do is illustrated here:
I start with A and B, then B is conformed to A to create C.
The idea is, given TLBR rectangles A, B, make C
I also need to know if it produces an empty rectangle (B outside of A case).
I tried this but it just isn't doing what I want:
if(clipRect.getLeft() > rect.getLeft())
L = clipRect.getLeft();
else
L = rect.getLeft();
if(clipRect.getRight() < rect.getRight())
R = clipRect.getRight();
else
R = rect.getRight();
if(clipRect.getBottom() > rect.getBottom())
B = clipRect.getBottom();
else
B = rect.getBottom();
if(clipRect.getTop() < rect.getTop())
T = clipRect.getTop();
else
T = rect.getTop();
if(L < R && B < T)
{
clipRect = AguiRectangle(0,0,0,0);
}
else
{
clipRect = AguiRectangle::fromTLBR(T,L,B,R);
}
Thanks
You seem to have a mistake in the final condition checking whether or not the intersection rectangle is empty.
You check L < R && B < T, but it seems like the condition for an empty rectangle should be:
L > R || B < T.
By the way, you can make your code a little simpler and easier to read by using Min and Max functions. You have a lot of this pattern:
if (x < y)
a = x;
else
a = y;
Which can be written simply as
a = Min(x, y);
Edit
Another mistake is that you take the maximum bottom and the minimum top. You should be taking the minimum bottom and the maximum top. (Assuming the rectangles correspond to screen coordinates, where the top actuallly has lower y values.
Logically, these are two different problems. I would first write an is_intersected() function returning an appropriate boolean value.
If the rects do intersect, I would then perform a clip operation that resembled the following pseudocode:
C.left.x = max(A.left.x, B.left.x);
C.right.x = min(A.right.x, B.right.x);
C.left.y = max(A.left.y, B.left.y);
C.right.y = min(A.right.y, B.right.y);
Related
For example, if a moving ball goes beyond the screen, what is the exact method to do it?
I currently do this:
if (x < 0.0) x = screenWidth() - 1;
else if (x >= screenWidth()) x = 0;
// same for y
But I saw this version:
if (x < 0.0) x = x + screenWidth();
else if (x >= screenWidth()) x = x - screenWidth();
// same for y
Isn't the second version doing useless addition/subtraction?
They do slightly different things: one does a cyclic wrapping (the second version) the other one just brings it to the edge (the first version).
Note that the code you are using for the cyclic wrapping may in general be wrong. Consider for example a screen_size = 800; and x = -10000;. Your code will bring it to x = -9200. You probably want to do x = x % screen_size before using your code for the cyclic wrapping, or you could use: ((x % screen_size) + screen_size) % screen_size instead.
In your version you just move the ball to the edge of the screen if it went out of it, but in the other version it keeps the distance that the balls travelled theoretically outside the screen to be considered in its new position. This helps to show the ball as travelling with the same speed.
I writing a program to numerically find the roots of functions with irrational roots by various methods.
For methods such as linear interpolation, you need to find the approximate range in which a root lies, for this I wrote this code:
bool fxn1 = false;
bool fxn2 = false;
vector<float> root_list;
if(f_x(-100) < 0)
{
fxn2 = true;
}
for(float i = -99.99; i < 100.01; i += 0.01)
{
fxn1 = fxn2;
if(f_x(i) < 0)
{
fxn2 = true;
}
else
{
fxn2 = false;
}
if((fxn1 == false && fxn2 == true) || (fxn1 == true && fxn2 == false))
{
root_list.push_back(i-0.01);
root_list.push_back(i);
}
}
However, for non-continuous functions (i.e. functions with asymptotes), this code will also be triggered when the function swaps from positive to negative values either side of the asymptote.
Is there a way to get the program to tell the difference between a root and an asymptote?
Thanks in advance
If the function, f(x), is converging on a point inside [a,b] then the half-way point (a + b) / 2 should be closer to zero than a or b.
This observation leads to the following procedure:
Let mid = (a + b) / 2
If |f(mid)| < |f(a)| AND |f(mid)| < |f(b)| Then
Algorithm has converged to a root
Else
Algorithm has converged to an asymptote
End
In this pseudo code |.| denotes floating-point absolute value.
Finding numerically a root only make sense if the function has nice properties, and at least is continuous. What would you think about this one:
f: x -> f(x) defined by:
2 * i < x < 2 * i + 1 (i element of Z) : f(x) = x
2 - i + 1 < x < 2 * i (i element of Z) : f(x) = -x
x = i (i element of Z) : f(x) = 1
It is perfectly defined on R, is bounded on any bounded interval, has positive and negative values on any interval of size > 1, and is continuous on any non integer point, but it has no root.
It is simply because the rule that a root must exist on segment ]x, y[ if x < 0 < y or y < 0 < x only applies if the function is continuous on the interval.
And good luck if you want to numerically test for continuity of a function...
I'm building a heatmap-like rectangular array interface and I want the 'hot' location to be at the top left of the array, and the 'cold' location to be at the bottom right. Therefore, I need an array to be filled diagonally like this:
0 1 2 3
|----|----|----|----|
0 | 0 | 2 | 5 | 8 |
|----|----|----|----|
1 | 1 | 4 | 7 | 10 |
|----|----|----|----|
2 | 3 | 6 | 9 | 11 |
|----|----|----|----|
So actually, I need a function f(x,y) such that
f(0,0) = 0
f(2,1) = 7
f(1,2) = 6
f(3,2) = 11
(or, of course, a similar function f(n) where f(7) = 10, f(9) = 6, etc.).
Finally, yes, I know this question is similar to the ones asked here, here and here, but the solutions described there only traverse and don't fill a matrix.
Interesting problem if you are limited to go through the array row by row.
I divided the rectangle in three regions. The top left triangle, the bottom right triangle and the rhomboid in the middle.
For the top left triangle the values in the first column (x=0) can be calculated using the common arithmetic series 1 + 2 + 3 + .. + n = n*(n+1)/2. Fields in the that triangle with the same x+y value are in the same diagonal and there value is that sum from the first colum + x.
The same approach works for the bottom right triangle. But instead of x and y, w-x and h-y is used, where w is the width and h the height of rectangle. That value have to be subtracted from the highest value w*h-1 in the array.
There are two cases for the rhomboid in the middle. If the width of rectangle is greater than (or equal to) the height, then the bottom left field of the rectangle is the field with the lowest value in the rhomboid and can be calculated that sum from before for h-1. From there on you can imagine that the rhomboid is a rectangle with a x-value of x+y and a y-value of y from the original rectangle. So calculations of the remaining values in that new rectangle are easy.
In the other case when the height is greater than the width, then the field at x=w-1 and y=0 can be calculated using that arithmetic sum and the rhomboid can be imagined as a rectangle with x-value x and y-value y-(w-x-1).
The code can be optimised by precalculating values for example. I think there also is one formula for all that cases. Maybe i think about it later.
inline static int diagonalvalue(int x, int y, int w, int h) {
if (h > x+y+1 && w > x+y+1) {
// top/left triangle
return ((x+y)*(x+y+1)/2) + x;
} else if (y+x >= h && y+x >= w) {
// bottom/right triangle
return w*h - (((w-x-1)+(h-y-1))*((w-x-1)+(h-y-1)+1)/2) - (w-x-1) - 1;
}
// rhomboid in the middle
if (w >= h) {
return (h*(h+1)/2) + ((x+y+1)-h)*h - y - 1;
}
return (w*(w+1)/2) + ((x+y)-w)*w + x;
}
for (y=0; y<h; y++) {
for (x=0; x<w; x++) {
array[x][y] = diagonalvalue(x,y,w,h);
}
}
Of course if there is not such a limitation, something like that should be way faster:
n = w*h;
x = 0;
y = 0;
for (i=0; i<n; i++) {
array[x][y] = i;
if (y <= 0 || x+1 >= w) {
y = x+y+1;
if (y >= h) {
x = (y-h)+1;
y -= x;
} else {
x = 0;
}
} else {
x++;
y--;
}
}
What about this (having an NxN matrix):
count = 1;
for( int k = 0; k < 2*N-1; ++k ) {
int max_i = std::min(k,N-1);
int min_i = std::max(0,k-N+1);
for( int i = max_i, j = min_i; i >= min_i; --i, ++j ) {
M.at(i).at(j) = count++;
}
}
Follow the steps in the 3rd example -- this gives the indexes (in order to print out the slices) -- and just set the value with an incrementing counter:
int x[3][3];
int n = 3;
int pos = 1;
for (int slice = 0; slice < 2 * n - 1; ++slice) {
int z = slice < n ? 0 : slice - n + 1;
for (int j = z; j <= slice - z; ++j)
x[j][slice - j] = pos++;
}
At a M*N matrix, the values, when traversing like in your stated example, seem to increase by n, except for border cases, so
f(0,0)=0
f(1,0)=f(0,0)+2
f(2,0)=f(1,0)+3
...and so on up to f(N,0). Then
f(0,1)=1
f(0,2)=3
and then
f(m,n)=f(m-1,n)+N, where m,n are index variables
and
f(M,N)=f(M-1,N)+2, where M,N are the last indexes of the matrix
This is not conclusive, but it should give you something to work with. Note, that you only need the value of the preceding element in each row and a few starting values to begin.
If you want a simple function, you could use a recursive definition.
H = height
def get_point(x,y)
if x == 0
if y == 0
return 0
else
return get_point(y-1,0)+1
end
else
return get_point(x-1,y) + H
end
end
This takes advantage of the fact that any value is H+the value of the item to its left. If the item is already at the leftmost column, then you find the cell that is to its far upper right diagonal, and move left from there, and add 1.
This is a good chance to use dynamic programming, and "cache" or memoize the functions you've already accomplished.
If you want something "strictly" done by f(n), you could use the relationship:
n = ( n % W , n / H ) [integer division, with no remainder/decimal]
And work your function from there.
Alternatively, if you want a purely array-populating-by-rows method, with no recursion, you could follow these rules:
If you are on the first cell of the row, "remember" the item in the cell (R-1) (where R is your current row) of the first row, and add 1 to it.
Otherwise, simply add H to the cell you last computed (ie, the cell to your left).
Psuedo-Code: (Assuming array is indexed by arr[row,column])
arr[0,0] = 0
for R from 0 to H
if R > 0
arr[R,0] = arr[0,R-1] + 1
end
for C from 1 to W
arr[R,C] = arr[R,C-1]
end
end
I have this assigment in university where I'm given the code of a C++ game involving pathfinding. The pathfinding is made using a wave function and the assigment requires me to make a certain change to the way pathfinding works.
The assigment requires the pathfinding to always choose the path farthest away from any object other than clear space. Like shown here:
And here's the result I've gotten so far:
Below I've posted the part of the Update function concerning pathfinding as I'm pretty sure that's where I'll have to make a change.
for (int y = 0, o = 0; y < LEVEL_HEIGHT; y++) {
for (int x = 0; x < LEVEL_WIDTH; x++, o++) {
int nCost = !bricks[o].type;
if (nCost) {
for (int j = 0; j < 4; j++)
{
int dx = s_directions[j][0], dy = s_directions[j][1];
if ((y == 0 && dy < 0)
|| (y == LEVEL_HEIGHT - 1 && dy > 0)
|| (x == 0 && dx < 0)
|| (x == LEVEL_WIDTH - 1 && dx > 0)
|| bricks[o + dy * LEVEL_WIDTH + dx].type)
{
nCost = 2;
break;
}
}
}
pfWayCost[o] = (float)nCost;
}
}
Also here is the Wave function if needed for further clarity on the problem.
I'd be very grateful for any ideas on how to proceed, since I've been struggling with this for quite some time now.
Your problem can be reduced to a problem known as minimum-bottle-neck-spanning-tree.
For the reduction do the following:
calculate the costs for every point/cell in space as the minimal distance to an object.
make a graph were edges correspond to the points in the space and the weights of the edges are the costs calculated in the prior step. The vertices of the graph corresponds to the boundaries between cell.
For one dimensional space with 4 cells with costs 10, 20, 3, 5:
|10|20|3|5|
the graph would look like:
A--(w=10)--B--(w=20)--C--(w=3)--D--(w=5)--E
With nodes A-E corresponding to the boundaries of the cells.
run for example the Prim's algorithm to find the MST. You are looking for the direct way from the entry point (in the example above A) to the exit point (E) in the resulting tree.
I have an algorithm which can find if a point is in a given polygon:
int CGlEngineFunctions::PointInPoly(int npts, float *xp, float *yp, float x, float y)
{
int i, j, c = 0;
for (i = 0, j = npts-1; i < npts; j = i++) {
if ((((yp[i] <= y) && (y < yp[j])) ||
((yp[j] <= y) && (y < yp[i]))) &&
(x < (xp[j] - xp[i]) * (y - yp[i]) / (yp[j] - yp[i]) + xp[i]))
c = !c;
}
return c;
}
given this, how could I make it check if its within a rectangle defind by Ptopleft and Pbottomright instead of a single point?
Thanks
Basically you know how in Adobe Illustrator you can drag to select all objects that fall within the selection rectangle? well I mean that. –
Can't you just find the minimum and maximum x and y values among the points of the polygon and check to see if any of the values are outside the rectangle's dimensions?
EDIT: duh, I misinterpreted the question. If you want to ensure that the polygon is encosed by a rectangle, do a check for each polygon point. You can do that more cheaply with the minimum/maximum x and y coordinates and checking if that rectangle is within the query rectangle.
EDIT2: Oops, meant horizontal, not vertical edges.
EDIT3: Oops #2, it does handle horizontal edges by avoiding checking edges that are horizontal. If you cross multiply however, you can avoid the special casing as well.
int isPointInRect( Point point, Point ptopleft, Point pbottomright) {
float xp[2] ;
xp[0] = ptopleft.x,
xp[1] = pbottomright.x;
float yp[2] ;
yp[0] = ptopleft.y ;
yp[1] = pbottomright.y ;
return CGlEngineFunctions::PointInPoly(2, xp, yp, point.x, point.y);
}
As mentioned before, for that specific problem, this function is an overkill. However, if you are required to use it, note that:
1. It works only for convex polygons,
2. The arrays holding the polygon's vertices must be sorted such that consecutive points in the array relate to adjacent vertices of your polygon.
3. To work properly, the vertices must be ordered in the "right hand rule" order. That means that when you start "walking" along the edges, you only make left turns.
That said, I think there is an error in the implementation. Instead of:
// c initialized to 0 (false), then...
c = !c;
you should have something like:
// c initialized to 1 (true), then...
// negate your condition:
if ( ! (....))
c = 0;