Help with some rotation matrix code :)

Discussion in 'Indie Basics' started by oddvark, Sep 11, 2007.

  1. oddvark

    Original Member

    Sep 27, 2004
    Likes Received:
    HI. I found the below code on the internet regarding constructing a rotation matrix around an arbitrary vector. My question is, what is MATRIX_Z? I'm gonna guess that is a rotation matrix around the z axis of the given angle. ..Does this sound right? Thanks.

    Heres the full article:

    WWH5: Calculating a Rotation Matrix Based on Location/Target
    by Paul Nettle

    The purpose of a WWH is to expand one's knowledge on a topic they already understand, but need a reference, a refresher course, or to simply extend what they already know about the topic.

    WWH is the quick tutor. Just the [W]hat, [W]hy and [H]ow
    WWH Calculating a rotation matrix based on location/target
    Text version 1.0
    Written by Paul Nettle (
    Last Modified May 15, 1997
    Prerequisites Basic vector and matrix mathematics

    The purpose here is to describe how to obtain a proper matrix given a location and a target (or a vector), and an amount of roll.

    This document will also emulate the specific nature of 3DS cameras, when it comes to the degenerate case (input vector points directly up).

    The accompanying source code is in C++.

    This is useful when dealing with cameras in a 3D world, or when you need to orient an object based on a vector, rather than roll/pitch/yaw components.

    cVector - dx, dy, dz
    cMatrix - 3x3 matrix class (consisting of 3 cVectors)

    The input Vector must be a directional vector. So for location->target, calculate like this:

    vector = target - camera;

    There is a problem with creating rotation matricies out of direction vectors. There is a degenerate case when the [delta y] of the direction vector is anything but zero. 3D Studio handles this in a special way, and here's a solution to it.

    Many people claim to have perfectly working code, and I have found that in over 50% of them, this was not the case.

    To test this, simply view an object from all 6 directions (above, below, left, right, front, back). Make sure the view vector contains two 0 components and a 1 component (i.e. [0,0,1] or [0,-1,0]).

    The degenerate cases are [0,1,0] and [0,-1,0]. Pay special attention to the degenerate cases.

    This code based on the descriptions in _Computer Graphics Principles and Practice_ (page 222) by Foley, van Dam, Feiner and Hughes.

    cMatrix cMatrix::generateMatrix( cVector &vector, const float rollDegrees )
    // Get our direction vector (the Z vector component of the matrix)
    // and make sure it's normalized into a unit vector

    cVector zAxis(vector);

    // Build the Y vector of the matrix (handle the degenerate case
    // in the way that 3DS does) -- This is not the TRUE vector, only
    // a reference vector.

    cVector yAxis;

    if (!zAxis.dx && !
    yAxis = cVector(-zAxis.dy, 0.0f, 0.0f );
    yAxis = cVector(0.0f, 1.0f, 0.0f);

    // Build the X axis vector based on the two existing vectors

    cVector xAxis = yAxis.cross( zAxis );

    // Correct the Y reference vector

    yAxis = xAxis.cross( zAxis );
    yAxis = -yAxis;

    // Generate rotation matrix without roll included

    cMatrix rot(xAxis, yAxis, zAxis);

    // Generate the Z rotation matrix for roll (bank)

    cMatrix roll(MATRIX_Z, rollDegrees);

    // Concatinate them for a complete rotation matrix that includes
    // all rotations

    cMatrix result = roll * rot;

    // All done

    return result;
    #1 oddvark, Sep 11, 2007
    Last edited: Sep 11, 2007
  2. WickedEwok

    Original Member

    Jul 7, 2005
    Likes Received:
    Since it's generating a rotation CMatrix first from 3 axis, then tries to generate another rotation matrix using MATRIX_Z and an angle, I assume it's an angle-axis representation and that Matrix_Z is a vector that probably just defines which basis vector is Z for your matrices?
  3. Nikster

    Original Member

    Jul 27, 2004
    Likes Received:
    Shouldn't this be in the "game development and technical" area ?
  4. princec

    Indie Author

    Jul 27, 2004
    Likes Received:
    No, it should be on

    Cas :)
  5. Feorang

    Feorang New Member

    Mar 13, 2017
    Likes Received:
    Looks like an overly complicated rotation function. Pick up an orbital mechanics book (they do the best for free rotation in 3 space) and pull the matrix ops. That math hasn't broken in 60 years, so you can consider it fairly reliable.

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