为何我的透视投影实现无法正确显示立方体的各个面？

Hey there, I totally get how frustrating it is to nail down perspective projection—even when you’ve got the theory locked in from tutorials, translating that into working code can throw all sorts of curveballs. Let’s break down some common pitfalls that might be tripping up your implementation, based on the techniques you mentioned:

• Homogeneous Coordinate Missteps
  It’s easy to mix up the order of operations when working with homogeneous coordinates. Remember that after applying your projection matrix, you need to perform perspective division (dividing the x, y, z components by the w component) to convert back to Cartesian coordinates for your 2D canvas. If you skip this step, or do it before applying the projection, your points will be wildly off. Also double-check that your projection matrix is correctly structured: make sure the focal length (or field of view) is properly incorporated, and that your near/far plane values are set logically (they shouldn’t be zero or negative unless you’re working on something specialized).

• Similar Triangle Calculation Errors
  When using similar triangles directly (instead of a matrix approach), nailing the reference distances is critical. Let’s say your camera sits at (0,0,d) looking along the negative z-axis: the projected x-coordinate on the canvas should be (x * focal_length) / (d + z)—but wait, depending on your coordinate system’s handedness, that sign might flip. If your 3D points have z-values increasing away from the camera, you might need (x * focal_length) / z instead. Mixing up the z-axis direction is a super common mistake here. Also make sure your focal length is scaled to match your canvas size: if your canvas is 800x600, a focal length of 500 might make sense, but 0.5 would just give you tiny, clustered points.

• Coordinate System Alignment
  3D world coordinates, camera coordinates, and 2D canvas coordinates don’t line up by default. Most 2D canvases have their origin at the top-left corner, while your 3D camera might use a center-origin system. You’ll need to translate and flip the projected y-coordinate (since canvas y-values increase downward) to get points in the right spot. Forget this step, and your points might be upside-down or entirely off-screen.

• Edge Cases & Debugging Tips
  Start testing with simple, predictable points to isolate issues:

  • A point at the camera’s position (e.g., (0,0,0) if that’s your camera origin) should project to the center of the canvas.
  • A point along the camera’s forward axis (like (0,0,100)) should also land at the center—points off-axis should get smaller as their z-distance from the camera increases.
  • Print out intermediate values: What’s the homogeneous coordinate before division? What are the x/y values after division? Do these match what you’d calculate manually?

Once you share your specific code snippets, plus details from those tutorials (like the coordinate systems they used or the exact projection formulas they taught), we can dig even deeper into what’s going wrong.

内容的提问来源于stack exchange，提问作者JarsOfJam-Scheduler