*\n * get projecting point of the point\n * */
时间: 2024-06-20 15:04:08 浏览: 100
"get projecting point of the point" 这个表述似乎是在询问如何找到某个点在某个投影或映射过程中的对应位置。这可能是几何、计算机图形学、摄影或者数学中的概念,具体取决于上下文。在三维空间中,如果涉及到投影,可能是指从三维空间到二维平面上的投影,如透视投影或平行投影。在计算机视觉中,这可能涉及到图像处理中的特征点投影。
简要解释一下,如果我们有一个三维空间中的点(x, y, z),要在另一个平面上找到它的投影,例如在屏幕上,我们通常会遵循一定的投影矩阵或公式,比如在透视投影中使用pinhole camera model。这个过程可能包括将三维坐标乘以一个投影矩阵,然后取结果的前两个分量作为二维平面上的投影点。
相关问题
Describe how to "squish" the frustum into a cuboid(n->n,f->f)
To "squish" a frustum into a cuboid, you would need to perform a process called perspective projection. This involves taking each point in the frustum and projecting it onto a flat plane that represents the cuboid.
The steps to do this are as follows:
1. Define the parameters of the frustum: the near plane distance (n), the far plane distance (f), the field of view angle (FOV), and the aspect ratio of the viewport.
2. Calculate the dimensions of the frustum. This involves using trigonometry to calculate the height and width of the near plane based on the FOV angle and aspect ratio, and then using similar triangles to calculate the height and width of the far plane.
3. Create a projection matrix. This is a 4x4 matrix that will be used to transform points in the frustum into the cuboid. The projection matrix can be created using the following formula:
```
P = [ 2n/(r-l) 0 (r+l)/(r-l) 0 ]
[ 0 2n/(t-b) (t+b)/(t-b) 0 ]
[ 0 0 -(f+n)/(f-n) -2fn/(f-n)]
[ 0 0 -1 0 ]
```
where l, r, b, and t are the coordinates of the left, right, bottom, and top edges of the near plane, respectively.
4. Apply the projection matrix to each point in the frustum. This involves multiplying each point by the projection matrix. The resulting points will be in homogenous coordinates, which can be converted to Cartesian coordinates by dividing by the fourth coordinate.
5. Map the resulting points onto the cuboid. To do this, you will need to define the dimensions of the cuboid (e.g. width, height, and depth). You can then map the x, y, and z coordinates of the transformed points to the corresponding ranges of the cuboid (e.g. x=-1 corresponds to the left side of the cuboid, x=1 corresponds to the right side, etc.)
6. Render the "squished" frustum. Once you have mapped the transformed points onto the cuboid, you can render the resulting scene as if it were a normal 3D scene. The "squishing" effect will be apparent due to the perspective projection.
We can now use a method to plot the loss surface of the network by projecting the parameter updates into two dimensions. You can find more information on that here. But you can just use the provided code. The contour plot will show how the loss will change if you would follow the two main directions of the past parameter updates. Think about the challenges and the optimization process of this landscape. What could impede the convergence of the net? # project states onto the main directions of the gradient updates using n samples over all steps starting from sample x # the directions are calculated using the last sample as a reference directions, state_ids, loss_coordinates = get_state_directions(states, n_states=10, start_from=0, reference_id=-1) # compute the losses over the main directions of the gradient updates x, y, Z, _ = get_loss_grid(net, data_loader, loss_fn, directions=directions, resolution=(20, 20), scale=loss_coordinates.abs().max().item()) # plot the landscape as a contour plot fig = plot_contour(np.copy(x), np.copy(y), np.copy(Z), scale=True) fig.add_traces(go.Scatter(x=np.copy(loss_coordinates[0].cpu().numpy()), y=np.copy(loss_coordinates[1].cpu().numpy()))) print('loss samples:', np.array(losses)[state_ids]) conf_pltly() init_notebook_mode(connected=False) iplot(fig) --------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) <ipython-input-62-26d05ea2d790> in <cell line: 3>() 1 # project states onto the main directions of the gradient updates using n samples over all steps starting from sample x 2 # the directions are calculated using the last sample as a reference ----> 3 directions, state_ids, loss_coordinates = get_state_directions(states, n_states=10, start_from=0, reference_id=-1) 4 5 # compute the losses over the main directions of the gradient updates <ipython-input-60-6cc4aad7dcda> in get_state_directions(states, n_states, start_from, reference_id) 15 params.append(param.view(-1)) 16 ---> 17 params = torch.stack(params, dim=0) 18 reference = params[-1] 19 RuntimeError: stack expects each tensor to be equal size, but got [200704] at entry 0 and [256] at entry 1这个错误怎么改
这个错误是由于在进行 torch.stack(params, dim=0) 操作时,params 中的张量维度不一致导致的。可以通过使用 torch.cat() 来代替 torch.stack(),将 params 列表中的张量按照指定维度拼接起来,从而避免这个错误。具体来说,可以将 get_state_directions() 函数中的 params = torch.stack(params, dim=0) 改为 params = torch.cat(params, dim=0)。