Original Post
So, I have a convex shaped thingy, and a triangle, I need to test if both have overlap. So, I convert the convex to triangles (cake), then do triangle-to-triangle overlap tests. But, it's kind of slow compared to some other code... The other code is: http://jgt.akpeters.com/papers/GuigueDevillers03/triangle_triangle_intersection.html However, it has a very vital bug (or, unpleasant feature, w/e you want to call it) which makes that even if triangles just touch, it says they intersect. Mathematically non-sense and is not what I want. Tried to see if I could fix it, but the code is a horror to maintain (or even look at). I'm very jealous about it's speed though, and I'd be very interested if anyone knew if this technique had a name, so I could rebuild it properly (err, maintainably). My test is like this: I check whether triangle line-segments intersect, and I check if any of them has points in each other, or 3 points on the borders of the other (on the edge or on a vertex). It works, I'm proud, and it's quite faster then that SAT (separate axis theorem) method. Yes, so basically, I'm looking into optimizing the current code. Does anyone know what the technique is called or where it is described of the above link? This is the code I currently am using. Basically, I do line-line intersection tests, if they succeed, we got overlap. Then I check if either one point is inside, or 3 points are on the borders. If so, JACKPOT! This handles about 7mil tri-tri overlap tests per second. Thanks! PS: performance drops significant if the convex object has multiple triangle (that is, not linear). Gprof:
inline
unsigned int point_in_triangle(Vertex point, Vertex triangle[3])
{
// from http://www.blackpawn.com/texts/pointinpoly/default.html
Vertex v0 = triangle[2] - triangle[0];
Vertex v1 = triangle[1] - triangle[0];
Vertex v2 = point - triangle[0];
double dot00 = dot(v0, v0);
double dot01 = dot(v0, v1);
double dot02 = dot(v0, v2);
double dot11 = dot(v1, v1);
double dot12 = dot(v1, v2);
double invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
double u = (dot11 * dot02 - dot01 * dot12) * invDenom;
double v = (dot00 * dot12 - dot01 * dot02) * invDenom;
if ((u > 0) && (v > 0) && (u + v < 1))
{
return 3;
}
else if ((u == 0) || (v == 0) || (u + v == 1))
{
return 1;
}
return 0;
}
inline
bool triangle_in_triangle(Vertex triangle1[3], Vertex triangle2[3])
{
unsigned int a = 0, b = 0;
for (unsigned int i = 0; i < 3; i++)
{
a += point_in_triangle(triangle1, triangle2);
if (a > 2)
{
return true;
}
b += point_in_triangle(triangle2, triangle1);
if (b > 2)
{
return true;
}
}
return false;
}
inline
bool triangle_intersects_triangle(Vertex triangle1[3], Vertex triangle2[3])
{
Vertex *a, *b, *c, *d;
double s, s_denominator;
double t, t_denominator;
//unsigned int match = 0, touch = 0;
for (unsigned int i = 0; i < 3; i++)
{
a = &triangle1
if (i != 2)
{
b = &triangle1[i + 1];
}
else
{
b = &triangle1[0];
}
for (unsigned int j = 0; j < 3; j++)
{
c = &triangle2[j];
if (j != 2)
{
d = &triangle2[j + 1];
}
else
{
d = &triangle2[0];
}
// since: a + s(b - a) = c + t(d - c) where t and s are scalars
// from this vector equation follow 3 normal equations (x, y and z)
// since we have 2 unknowns, we can scrap one equation for being dependant
s_denominator = ((b->y - a->y) * (d->x - c->x) - (b->x - a->x) * (d->y - c->y));
if (s_denominator)
{
s = ((c->y - a->y) * (d->x - c->x) + (a->x - c->x) * (d->y - c->y)) / s_denominator;
if (s > 0 && s < 1)
{
t_denominator = ((d->y - c->y) * (b->x - a->x) - (d->x - c->x) * (b->y - a->y));
if (t_denominator)
{
t = ((a->y - c->y) * (b->x - a->x) + (c->x - a->x) * (b->y - a->y)) / t_denominator;
if (t > 0 && t < 1)
{
return true; // edges intersect
}
}
}
}
}
}
return false;
}
inline
bool triangle_overlaps_triangle(Vertex triangle1[3], Vertex triangle2[3])
{
if (triangle_intersects_triangle(triangle1, triangle2))
{
return true;
}
else if (triangle_in_triangle(triangle1, triangle2))
{
return true;
}
return false;
}
bool triangle_overlaps_convex(Vertex triangle[3], Vertex *convex, unsigned int n)
{
if (n > 2) // has it got any surface?
{
unsigned int changing = 0, // next changing vertex of convex triangle
cw_i = 1, // current vertex clockwise
ccw_i = n - 1; // current vertex counter clockwise
Vertex convex_triangle[3] = {convex[0], convex[1], convex[n - 1]};
bool is_cw[3] = {true, true, false}; // which convex triangle vertices do currently use cw or ccw value
// go through all neccessary triangles within the convex to cover the whole convex
for (unsigned int i = 0; i < (n - 2); i++) // n - 2 triangles
{
if (triangle_overlaps_triangle(triangle, convex_triangle))
{
return true;
}
if (i < (n - 3))
{
if (is_cw[changing])
{
ccw_i--;
convex_triangle[changing] = convex[ccw_i];
is_cw[changing] = false;
}
else
{
cw_i++;
convex_triangle[changing] = convex[cw_i];
is_cw[changing] = true;
}
changing++;
if (changing == 3)
{
changing = 0;
}
}
}
}
return false;
}
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ns/call ns/call name
27.69 0.72 0.72 3000000 240.00 240.00 triangle_intersects_triangle(Vertex*, Vertex*)
25.77 1.39 0.67 50000000 13.40 13.40 dot(Vertex const&, Vertex const&)
16.92 1.83 0.44 30000000 14.67 20.67 Vertex::operator-(Vertex const&) const
13.08 2.17 0.34 10000000 34.00 163.00 point_in_triangle(Vertex, Vertex*)
6.92 2.35 0.18 30000042 6.00 6.00 Vertex::Vertex(double, double, double)
3.85 2.45 0.10 3000000 33.33 850.00 triangle_overlaps_convex(Vertex*, Vertex*, unsigned int)
3.46 2.54 0.09 2000000 45.00 860.00 triangle_in_triangle(Vertex*, Vertex*)
1.15 2.57 0.03 cross(Vertex const&, Vertex const&)
0.77 2.59 0.02 main
0.38 2.60 0.01 3000000 3.33 816.67 triangle_overlaps_triangle(Vertex*, Vertex*)
0.00 2.60 0.00 2 0.00 0.00 GetTime()
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Call graph (explanation follows)
granularity: each sample hit covers 4 byte(s) for 0.38% of 2.60 seconds
index % time self children called name
<spontaneous>
[1] 98.8 0.02 2.55 main [1]
0.10 2.45 3000000/3000000 triangle_overlaps_convex(Vertex*, Vertex*, unsigned int) [2]
0.00 0.00 42/30000042 Vertex::Vertex(double, double, double) [9]
0.00 0.00 2/2 GetTime() [14]
-----------------------------------------------
0.10 2.45 3000000/3000000 main [1]
[2] 98.1 0.10 2.45 3000000 triangle_overlaps_convex(Vertex*, Vertex*, unsigned int) [2]
0.01 2.44 3000000/3000000 triangle_overlaps_triangle(Vertex*, Vertex*) [3]
-----------------------------------------------
0.01 2.44 3000000/3000000 triangle_overlaps_convex(Vertex*, Vertex*, unsigned int) [2]
[3] 94.2 0.01 2.44 3000000 triangle_overlaps_triangle(Vertex*, Vertex*) [3]
0.09 1.63 2000000/2000000 triangle_in_triangle(Vertex*, Vertex*) [4]
0.72 0.00 3000000/3000000 triangle_intersects_triangle(Vertex*, Vertex*) [6]
-----------------------------------------------
0.09 1.63 2000000/2000000 triangle_overlaps_triangle(Vertex*, Vertex*) [3]
[4] 66.2 0.09 1.63 2000000 triangle_in_triangle(Vertex*, Vertex*) [4]
0.34 1.29 10000000/10000000 point_in_triangle(Vertex, Vertex*) [5]
-----------------------------------------------
0.34 1.29 10000000/10000000 triangle_in_triangle(Vertex*, Vertex*) [4]
[5] 62.7 0.34 1.29 10000000 point_in_triangle(Vertex, Vertex*) [5]
0.67 0.00 50000000/50000000 dot(Vertex const&, Vertex const&) [7]
0.44 0.18 30000000/30000000 Vertex::operator-(Vertex const&) const [8]
-----------------------------------------------
0.72 0.00 3000000/3000000 triangle_overlaps_triangle(Vertex*, Vertex*) [3]
[6] 27.7 0.72 0.00 3000000 triangle_intersects_triangle(Vertex*, Vertex*) [6]
-----------------------------------------------
0.67 0.00 50000000/50000000 point_in_triangle(Vertex, Vertex*) [5]
[7] 25.8 0.67 0.00 50000000 dot(Vertex const&, Vertex const&) [7]
-----------------------------------------------
0.44 0.18 30000000/30000000 point_in_triangle(Vertex, Vertex*) [5]
[8] 23.8 0.44 0.18 30000000 Vertex::operator-(Vertex const&) const [8]
0.18 0.00 30000000/30000042 Vertex::Vertex(double, double, double) [9]
-----------------------------------------------
0.00 0.00 42/30000042 main [1]
0.18 0.00 30000000/30000042 Vertex::operator-(Vertex const&) const [8]
[9] 6.9 0.18 0.00 30000042 Vertex::Vertex(double, double, double) [9]
-----------------------------------------------
<spontaneous>
[10] 1.2 0.03 0.00 cross(Vertex const&, Vertex const&) [10]
-----------------------------------------------
0.00 0.00 2/2 main [1]
[14] 0.0 0.00 0.00 2 GetTime() [14]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Index by function name
[5] point_in_triangle(Vertex, Vertex*) [6] triangle_intersects_triangle(Vertex*, Vertex*) [9] Vertex::Vertex(double, double, double)
[4] triangle_in_triangle(Vertex*, Vertex*) [7] dot(Vertex const&, Vertex const&) [8] Vertex::operator-(Vertex const&) const
[2] triangle_overlaps_convex(Vertex*, Vertex*, unsigned int) [10] cross(Vertex const&, Vertex const&) [1] main
[3] triangle_overlaps_triangle(Vertex*, Vertex*) [14] GetTime()
