"""
Robot–environment convex collision in **xy** (ground plane).

For an **axis-aligned robot footprint** vs. a **single convex obstacle triangle**, a
**separating-axis test (SAT)** gives the same **intersection predicate** as **GJK** in
2D, with a compact fully batched reference. A fused device kernel often implements
**GJK (+ EPA for penetration depth)** for arbitrary 3D polyhedra; this problem is
the canonical 2D footprint special case.
"""

import torch
import torch.nn as nn

# Default ModelNew is PyTorch-only. run_and_check: use check_kernel=False with backend=cuda


def _rect_corners_xy(robot_min: torch.Tensor, robot_max: torch.Tensor) -> torch.Tensor:
    """(B, 4, 2) corners of axis-aligned rectangles."""
    x0, x1 = robot_min[:, 0], robot_max[:, 0]
    y0, y1 = robot_min[:, 1], robot_max[:, 1]
    return torch.stack(
        (
            torch.stack((x0, y0), dim=-1),
            torch.stack((x1, y0), dim=-1),
            torch.stack((x1, y1), dim=-1),
            torch.stack((x0, y1), dim=-1),
        ),
        dim=1,
    )


def _project_min_max(points: torch.Tensor, axis: torch.Tensor) -> tuple[torch.Tensor, torch.Tensor]:
    """points (B, K, 2), axis (B, 2) or (2,) broadcast → (B,) min and max projections."""
    if axis.dim() == 1:
        axis = axis.view(1, 2).expand(points.shape[0], -1)
    proj = (points * axis.unsqueeze(1)).sum(dim=-1)
    return proj.min(dim=-1).values, proj.max(dim=-1).values


def _batched_sat_rect_triangle(
    robot_min: torch.Tensor,
    robot_max: torch.Tensor,
    env_triangle: torch.Tensor,
    eps: float,
) -> torch.Tensor:
    """
    Separating-axis test: AABB vs triangle in 2D, fully vectorized over batch.
    Returns (B,) float 1.0 if overlapping else 0.0.
    """
    B = robot_min.shape[0]
    corners = _rect_corners_xy(robot_min, robot_max)
    hit = torch.ones(B, device=robot_min.device, dtype=robot_min.dtype)

    # World axes (rectangle is AABB)
    for ax in (
        torch.tensor([1.0, 0.0], device=robot_min.device, dtype=robot_min.dtype),
        torch.tensor([0.0, 1.0], device=robot_min.device, dtype=robot_min.dtype),
    ):
        r0, r1 = _project_min_max(corners, ax)
        t0, t1 = _project_min_max(env_triangle, ax)
        separated = (r1 < t0 - eps) | (t1 < r0 - eps)
        hit = hit * (~separated).to(hit.dtype)

    # Triangle edge normals (per batch)
    for i in range(3):
        e = env_triangle[:, (i + 1) % 3] - env_triangle[:, i]
        n = torch.stack((-e[:, 1], e[:, 0]), dim=-1)
        n = n / (n.norm(dim=-1, keepdim=True) + 1e-8)
        r0, r1 = _project_min_max(corners, n)
        t0, t1 = _project_min_max(env_triangle, n)
        separated = (r1 < t0 - eps) | (t1 < r0 - eps)
        hit = hit * (~separated).to(hit.dtype)

    return hit


class Model(nn.Module):
    """
    **Batched robot footprint vs. environment triangle** intersection in **xy**.

    Robot: axis-aligned box ``[robot_min, robot_max]`` per batch element.
    Environment: one **triangle** ``(B, 3, 2)``.

    Reference: **vectorized SAT** (5 axis tests). Fused-kernel target: same
    predicate via **GJK/EPA** or specialized SAT SIMD for planning loops.
    """

    def __init__(self, eps: float = 1e-6):
        super().__init__()
        self.eps = eps

    def forward(
        self,
        robot_min: torch.Tensor,
        robot_max: torch.Tensor,
        env_triangle: torch.Tensor,
    ) -> torch.Tensor:
        """
        Args:
            robot_min: (B, 2), robot_max: (B, 2) with max >= min componentwise.
            env_triangle: (B, 3, 2) obstacle vertices in order (any consistent winding).
        Returns:
            (B, 1) float in ``{0.0, 1.0}`` — **1** if the sets intersect.
        """
        B = robot_min.shape[0]
        assert robot_max.shape == (B, 2) and env_triangle.shape == (B, 3, 2)
        h = _batched_sat_rect_triangle(robot_min, robot_max, env_triangle, self.eps)
        return h.unsqueeze(-1)


class ModelNew(nn.Module):
    """KernelBench candidate entry point; default delegates to ``Model``."""

    def __init__(self, eps: float = 1e-6):
        super().__init__()
        self._impl = Model(eps=eps)

    def forward(
        self,
        robot_min: torch.Tensor,
        robot_max: torch.Tensor,
        env_triangle: torch.Tensor,
    ) -> torch.Tensor:
        return self._impl(robot_min, robot_max, env_triangle)


batch_size = 16


def get_inputs():
    bs = popcorn_pri.jitter_int(batch_size)
    robot_min = torch.empty(bs, 2).uniform_(-1.0, 0.5)
    robot_max = robot_min + torch.empty(bs, 2).uniform_(0.2, 0.8)
    env_triangle = torch.empty(bs, 3, 2).uniform_(-0.8, 0.8)
    return [robot_min, robot_max, env_triangle]


def get_init_inputs():
    return []

import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

_cuda_source = r'''
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <math.h>

__global__ void sat_kernel(
    const float* __restrict__ robot_min,
    const float* __restrict__ robot_max,
    const float* __restrict__ env_tri,
    float* __restrict__ output,
    const int B,
    const float eps
) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx >= B) return;

    float rmin0 = robot_min[2 * idx];
    float rmin1 = robot_min[2 * idx + 1];
    float rmax0 = robot_max[2 * idx];
    float rmax1 = robot_max[2 * idx + 1];

    float t0x = env_tri[6 * idx + 0];
    float t0y = env_tri[6 * idx + 1];
    float t1x = env_tri[6 * idx + 2];
    float t1y = env_tri[6 * idx + 3];
    float t2x = env_tri[6 * idx + 4];
    float t2y = env_tri[6 * idx + 5];

    bool hit = true;

    // Axis X
    float tmin = fminf(fminf(t0x, t1x), t2x);
    float tmax = fmaxf(fmaxf(t0x, t1x), t2x);
    if (rmax0 < tmin - eps || tmax < rmin0 - eps) hit = false;

    // Axis Y
    if (hit) {
        tmin = fminf(fminf(t0y, t1y), t2y);
        tmax = fmaxf(fmaxf(t0y, t1y), t2y);
        if (rmax1 < tmin - eps || tmax < rmin1 - eps) hit = false;
    }

    // Triangle edge normals
    float tx[3] = {t0x, t1x, t2x};
    float ty[3] = {t0y, t1y, t2y};
    for (int i = 0; i < 3 && hit; ++i) {
        int j = (i + 1) % 3;
        float ex = tx[j] - tx[i];
        float ey = ty[j] - ty[i];
        float nx = -ey;
        float ny = ex;
        float len = sqrtf(nx * nx + ny * ny) + 1e-8f;
        nx /= len;
        ny /= len;

        // Rect projections
        float p0 = rmin0 * nx + rmin1 * ny;
        float p1 = rmax0 * nx + rmin1 * ny;
        float p2 = rmax0 * nx + rmax1 * ny;
        float p3 = rmin0 * nx + rmax1 * ny;
        float rpmin = fminf(fminf(p0, p1), fminf(p2, p3));
        float rpmax = fmaxf(fmaxf(p0, p1), fmaxf(p2, p3));

        // Tri projections
        float tp0 = tx[0] * nx + ty[0] * ny;
        float tp1 = tx[1] * nx + ty[1] * ny;
        float tp2 = tx[2] * nx + ty[2] * ny;
        tmin = fminf(fminf(tp0, tp1), tp2);
        tmax = fmaxf(fmaxf(tp0, tp1), tp2);

        if (rpmax < tmin - eps || tmax < rpmin - eps) hit = false;
    }

    output[idx] = hit ? 1.0f : 0.0f;
}

torch::Tensor sat_cuda(torch::Tensor robot_min, torch::Tensor robot_max, torch::Tensor env_triangle, float eps) {
    const int B = robot_min.size(0);
    auto output = torch::empty({B, 1}, robot_min.options());

    const int threads = 256;
    const int blocks = (B + threads - 1) / threads;

    sat_kernel<<<blocks, threads>>>(
        robot_min.data_ptr<float>(),
        robot_max.data_ptr<float>(),
        env_triangle.data_ptr<float>(),
        output.data_ptr<float>(),
        B,
        eps
    );

    return output;
}
'''

_cpp_source = r'''
torch::Tensor sat_cuda(torch::Tensor robot_min, torch::Tensor robot_max, torch::Tensor env_triangle, float eps);
'''

_mod = load_inline(
    name="sat_cuda_mod",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["sat_cuda"],
    verbose=False,
    extra_cuda_cflags=["-O3"]
)

class ModelNew(nn.Module):
    def __init__(self, eps: float = 1e-6):
        super().__init__()
        self.eps = eps

    def forward(
        self,
        robot_min: torch.Tensor,
        robot_max: torch.Tensor,
        env_triangle: torch.Tensor,
    ) -> torch.Tensor:
        return _mod.sat_cuda(robot_min, robot_max, env_triangle, self.eps)
```