Introduction:

This tutorial is designed for someone with a small background in 3d matrix math and preferably with experience dealing with child-parent relationships within objects. A good example of this type of relationship would be skeletal systems.

There are 6 parts covering everything from setting up the software 3d development scene to displaying our final tree in an OpenGL scene. We'll be covering Parts 1 and 2 in this issue.

Part 1 'Base Code': Providing the base code for a simple 3d scene.

Part 2 'Planning': The makeup of a tree and how we plan to display our end product.

Part 3 'Branch Skeleton': Development of our branch system to make a very basic display of a parent-child skeletal system that will become our tree.

Part 4 'Leaf Planes': Creation of our leaf planes.

Part 5 'Branch Skinning': Skinning our tree skeleton and saving the mesh information

Part 6 'Final OpenGL Scene': Creating the OpenGL scene to display our mesh

Part 1: 'Base Code'

In order to properly see all the branches we must setup a 3d scene that we can change our viewing angle of. We'll also be able to Zoom in & out of the scene to aid in viewing the entire tree.

The following code will establish a software 3d environment showing a pixel grid floor. This grid consists of points on the X and Z axis with a 0 y coordinate. We will be constructing our tree to stick out of this floor by moving + on the y axis.

CONTROLS:

Rotate scene: arrow keys

Scale scene: +/-

I will only provide a simple explanation on the functions of this code that will directly affect our progress later

    mIdentity
    mRotate yan!, yplane
    mRotate xan!, xplane
    mScale matrixScale!

These commands will setup our matrix to properly convert 3d coordinates to our rotated and scaled view

    getXY x!, 0, z!, sx, sy
    PSET (sx, sy), 7

getXY will multiply our 3d coordinate by our matrix and spit out a screen coordinate which Pset draws

    if multikey(&h1) then exit do
    
    if multikey(&h48) then xan! = xan! + rotSpd!
    if multikey(&h50) then xan! = xan! - rotSpd!
    if multikey(&h4b) then yan! = yan! - rotSpd!
    if multikey(&h4d) then yan! = yan! + rotSpd!
    
    if multikey(&h4e) then matrixScale! = matrixScale! + scaleSpd!
    if multikey(&h4a) then matrixScale! = matrixScale! - scaleSpd!

    while inkey$ <> "": wend

We will be using multikey extensively since it provides a much faster response time than inkey$. the last line clears the keyboard buffer so that on our next cycle we detect only new keys that were pressed for that cycle.

I wont be explaining how the 3d math functions work to save writing, but if at the current time you do not understand the theory behind 3d matrix math I highly recommend doing some research on the subject. Rel has written some awesome tutorials that you can find here http://rel.betterwebber.com/junk.php?id=21

Part 2: 'Planning'

Branches:

The Idea is to have a branch made up of several segments. At any of the segments a new branch can be attached. The further you get away from the base of the branch the smaller the diameter of the branch and length of each segment become. Also, the base of a branch will start out at the diameter of the point that it is connected to. Lastly, since we don't want a really long branch to have a base at a point toward the end of a branch, we'll limit the number segments that a branch can have based on what segment its base is connected to

Leaves:

The leaves are made up of flat squares that are displayed over the branches. The center of each plane is positioned around a random joint on a random branch. The plane will be placed at a point that is > 1/2 along the branches to ensure that the leaves are in the upper part of the tree and not on the trunk. Next, the plane is rotated opposite the direction of the object and camera in order to make them constantly face forward. Then once the engine is displaying the tree in openGL, the leaves will be z-sorted and blended together.

I hope I didn't lose anyone. Just incase, here is a picture to hopefully give a good visual representation.

End Product:

For the final mesh, we will make a 'skin' around the branch skeleton by finding points that are perpendicular to each segment connection, then draw a cylinder connecting each segment. At the base, instead of a cylinder we'll have the 1st segment's cylinder come to a point to make a cone. These cones will be stuck into the parent branch segment base point. In order to make the polygons display properly in openGL we'll also generate UV coordinates and Normal vectors for each vertex.