"""
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 = """
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>

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

    // Load robot min/max
    float rx0 = robot_min[2*i];
    float ry0 = robot_min[2*i + 1];
    float rx1 = robot_max[2*i];
    float ry1 = robot_max[2*i + 1];

    // Load triangle vertices
    float tx[3], ty[3];
    for (int v = 0; v < 3; ++v) {
        tx[v] = env_triangle[6*i + 2*v];
        ty[v] = env_triangle[6*i + 2*v + 1];
    }

    bool overlap = true;

    // Axis 1: x-axis (1,0)
    {
        float rmin = rx0, rmax = rx1;
        float tmin = fminf(fminf(tx[0], tx[1]), tx[2]);
        float tmax = fmaxf(fmaxf(tx[0], tx[1]), tx[2]);
        if (rmax < tmin - eps || tmax < rmin - eps) overlap = false;
    }

    // Axis 2: y-axis (0,1)
    if (overlap) {
        float rmin = ry0, rmax = ry1;
        float tmin = fminf(fminf(ty[0], ty[1]), ty[2]);
        float tmax = fmaxf(fmaxf(ty[0], ty[1]), ty[2]);
        if (rmax < tmin - eps || tmax < rmin - eps) overlap = false;
    }

    // Triangle edge normals
    if (overlap) {
        for (int e = 0; e < 3; ++e) {
            int v0 = e;
            int v1 = (e + 1) % 3;
            float ex = tx[v1] - tx[v0];
            float ey = ty[v1] - ty[v0];
            float nx = -ey;
            float ny = ex;
            float nlen = sqrtf(nx*nx + ny*ny) + 1e-8f;
            nx /= nlen;
            ny /= nlen;

            // Project rect corners
            float rprojs[4];
            rprojs[0] = rx0 * nx + ry0 * ny;
            rprojs[1] = rx1 * nx + ry0 * ny;
            rprojs[2] = rx1 * nx + ry1 * ny;
            rprojs[3] = rx0 * nx + ry1 * ny;
            float rmin = fminf(fminf(rprojs[0], rprojs[1]), fminf(rprojs[2], rprojs[3]));
            float rmax = fmaxf(fmaxf(rprojs[0], rprojs[1]), fmaxf(rprojs[2], rprojs[3]));

            // Project triangle
            float tprojs[3];
            for (int v = 0; v < 3; ++v) {
                tprojs[v] = tx[v] * nx + ty[v] * ny;
            }
            float tmin = fminf(fminf(tprojs[0], tprojs[1]), tprojs[2]);
            float tmax = fmaxf(fmaxf(tprojs[0], tprojs[1]), tprojs[2]);

            if (rmax < tmin - eps || tmax < rmin - eps) {
                overlap = false;
                break;
            }
        }
    }

    output[i] = overlap ? 1.0f : 0.0f;
}

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

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

    sat_rect_triangle_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 = """
torch::Tensor sat_rect_triangle_cuda(
    torch::Tensor robot_min,
    torch::Tensor robot_max,
    torch::Tensor env_triangle,
    float eps
);
"""

module = load_inline(
    name='sat_module',
    cpp_sources=cpp_source,
    cuda_sources=cuda_source,
    functions=['sat_rect_triangle_cuda'],
    verbose=False
)

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 module.sat_rect_triangle_cuda(robot_min, robot_max, env_triangle, self.eps)