An Example of a Parameterized Polygon
(A parameterized polygons is defined by a contour and a set of constraints.)
The Number of Vertices: 67
The Number of Trapezoids: 33
Contour
| g,
c+2d-3e+10-a g+4d, c-2d-3e+10-a g+4d, c-6d-3e+10-a f, c-6d-3e+10-a f, s 10000, s 10000, c+2d-3e+10-a 10000-a, c+2d-3e+10-a 10000, c+2d-3e+10 10000+4d+a, c-2d-3e+10-a 10000+a, c-6d-3e+10-a 10000+4d+a, c-6d-3e+10-a 10000+4d+a, q t, q t, u 10000+3m-3n, u 10000+3m-3n, i v, i v, q-c+2d+3e-10+a+q 10000+m-n, q-c+2d+3e-10+a+q 10000+m-n, i-j w, i-j w, i-6d v, i-6d v, q-c+2d+3e-10+a+q-2a+2d p-2d+2a, q-c+2d+3e-10+a+q-2a+2d p, q-c+2d+3e-10+a+q p-2d+2a, q p, c-2d-3e+10-a p+4d+a, c+2d-3e+10 p+4d+2a, c+2d-3e+10-a p-2d+2a, c-4d-3e+10-a p-2d+2a+q-i, q p-2d+2a, i p+4d+2a, i-6d 10000+4m-4n, n 10000+3m-3n, m 2m-2n+10000, n m+10000-n, m 10000+m-n, n 10000, m 10000, q-c+2d+3e-10+a+q-2a+2d g+4d, q-c+2d+3e-10+a+q-2a+2d g+4d, m h, m h, q-c+2d+3e-10+a+q-2a+2d h-k, q-c+2d+3e-10+a+q-2a+2d-k h-k, i-j r, i-j r, i-6d g+4d+2j, i-6d g+4d+2j, i g+4d+j, i-j g+4d, i g, i g, q-c+2d+3e-10+a+q r, q-c+2d+3e-10+a+q r, i g-4d, i g-4d, q-c+2d+3e-10+a+q h, q-c+2d+3e-10+a+q h, q g+2d, q g+2d, c-4d-3e+10-a g, c-2d-3e+10-a g-4d, c-6d-3e+10-a g-4d, c-2d-3e+10-a |
Constraints
| 1 <= a
<= 100 1 <= c <= 100 1 <= d <= 10 1 <= e <= 10 1 <= f <= 1000 1 <= g <= 1000 1 <= h <= 1000 1 <= i <= 1000 1 <= j <= 1000 1 <= k <= 1000 1 <= m <= 1000 1 <= n <= 1000 10001 <= p <= 90000 1 <= q <= 1000 1 <= r <= 1000 1 <= s <= 1000 1 <= t <= 90000 1 <= u <= 1000 1 <= v <= 90000 1 <= w <= 90000 f > g+4d s > c-2d-3e+10-a s < c+2d-3e+10-a s > q q < c-6d-3e+10-a t > 10000+4d+a t < 10000+3m-3n 4d+a == 2m-2n v < 10000+m-n v > 10000 w < 10000+2m-2n w > 10000+m-n s > q-c+2d+3e-10+a+q 2a-2d == c-2d-3e+10-a-q m < q-c+2d+3e-10+a+q-2a+2d-k c-6d-3e+10-a > q-c+2d+3e-10+a+q-2a+2d i > q-c+2d+3e-10+a+q q-c+2d+3e-10+a+q > i-j i-j > i-6d i-6d-n == 2a+4d+p-10000-4m+4n i-6d > q-c+2d+3e-10+a+q-2a+2d r < g r > g-4d k < i-6d-m p > t p < p-2d+2a h < g-4d m > n i < u u < q 4m-4n+10000 < 2a-2d+p-q+u c-6d-3e+10-a < s q < c-2d-3e+10-a u < c-6d-3e+10-a v < 10000+3m-3n c+2d-3e+10 > s c+2d-3e+10 > c+2d-3e+10-a s > q-c+2d+3e-10+a+q-2a+2d s > q-c+2d+3e-10+q-a i < c-6d-3e+10-a a-c+2d+3e+2q-10 < c-6d-3e+10-a a-c+2d+3e+2q-10 < u i-6d < c-6d-3e+10-a i-6d < a-c+2d+3e+2q-10 v < w 4d+3e+2q-10-a-c < q 4d+3e+2q-10-a-c < i 4d+3e+2q-10-a-c < i-j 2a-2d+p > v p > v p > m-n+10000 2a-2d+p > t c-4d-3e+10-a < s 2a-2d-i+p+q > t 2a-2d+p > 3m-3n+10000 h < r f > c+2d-3e+g-1s+10-a a < 16d-c+3e-i+2q-10 |
The Result After Partitioning
last update: December 26, 2009