{"id":132,"date":"2015-09-07T23:43:22","date_gmt":"2015-09-07T23:43:22","guid":{"rendered":"http:\/\/metareal.net\/blog\/?p=132"},"modified":"2015-09-07T23:43:22","modified_gmt":"2015-09-07T23:43:22","slug":"which-way-is-up","status":"publish","type":"post","link":"http:\/\/metareal.net\/blog\/?p=132","title":{"rendered":"Which Way Is Up?"},"content":{"rendered":"

Metareal lets you maneuver unhindered in three dimensional space. There is no gravity, no walking. (And no head-bobbing.) It’s perhaps like a drone moving through a space station.<\/p>\n

But I wanted to keep the movement simple and easy. The familiar four-key-and-mouse maneuvering works pretty well, after all.<\/p>\n

Problem 1: Nearest Ground Plane<\/h2>\n

The solution was to treat the mouse relative movements as side-to-side, and up-and-down, relative to the dominant ground plane<\/i>. It turns out that figuring out which ground plane is best is pretty easy! The camera position and angle can be expressed as a conventional 4×4 column major matrix. From this, we look at the second column, which is where the camera’s Y-Up vector gets mapped to, and see which element has the greatest magnitude. It is that simple!<\/i><\/p>\n

For example,<\/p>\n

\n   \/                                  \\\n   |   0.826   0.070  -0.559   48.700 |\n   |   0.563  -0.103   0.820  -22.325 |\n   |   0.000  -0.992<\/b>  -0.125   -0.921 |\n   |   0.000   0.000   0.000    1.000 |\n   \\                                  \/\n<\/pre>\n
We can see for this matrix the bolded value -0.992 shows negative-Z as the dominant Up-vector.  So, mouse left and right motions apply, inverted, to the camera’s global Z-rotation. (Arithmetically, we translate the matrix to origin, rotate around global Z, and translate the matrix back to the camera position.)<\/p>\n
Problem 2: Don’t go diagonal!<\/h2>\n
\"OopsDiagonal\"<\/p>\n
A problem with this approach is you can end up stuck in a “roll”, where, on the new ground plane, you’re not standing upright. Or, rather, you<\/i> are standing upright, and if you spin left and right the floor stays beneath you, but your head<\/i> is tilted. To fix this, we need to discover what is our local-Z-rotation relative to the current ground plane. To correct it, we want to rotate the camera along its line of sight, not changing what it is looking at.<\/p>\n
\"RollQuestion\" \"RollQuestion3\"<\/p>\n
A little vector arithmetic does the trick; we cast the camera’s projected X-axis to the ground plane along the projected Y-axis (up vector), and take the dot product between the X-axis and its line along the ground plane. That’s how much we need to roll. Easy! But how to apply the correction?<\/p>\n
Problem 3: Correct The Up-Axis Naturally<\/h2>\n
I tried three approaches to correcting the up-axis, so that you’re usually looking at square walls and doors and things.<\/p>\n
    \n
  • Manual correction: use some more keyboard keys to roll left and roll right. Terrible! I didn’t like it, anyway.<\/li>\n
  • Automatic continuous correction: apply some radians-per-second maximum to correcting the roll. It’s ok, but adds a strange smoothness to your image movement sometimes…<\/li>\n
  • Proportional correction: apply some correction but limited by how much you’re moving the camera yourself. This way the camera never moves except when you’re moving it.<\/li>\n<\/ul>\n
    I’m not sure which is best, but I documented all three in a short video.<\/p>\n