The Matrix Behind 3D Engineering Graphics
𝗢𝗻𝗲 𝘀𝗶𝗺𝗽𝗹𝗲 𝗺𝗮𝘁𝗿𝗶𝘅. 𝗙𝗿𝗼𝗺 𝟯𝗗 𝘄𝗼𝗿𝗹𝗱𝘀 𝘁𝗼 𝗺𝗼𝗱𝗲𝗿𝗻 𝘀𝘁𝗿𝘂𝗰𝘁𝘂𝗿𝗮𝗹 𝗮𝗻𝗮𝗹𝘆𝘀𝗶𝘀 𝘀𝗼𝗳𝘁𝘄𝗮𝗿𝗲.
𝟭. 𝗜𝘁 𝘀𝘁𝗮𝗿𝘁𝘀 𝘄𝗶𝘁𝗵 𝗮 𝗽𝗼𝗶𝗻𝘁.
The formula in the image does two things:
• It rotates a point around Z.
• It moves the point along X, Y and Z.
Apply the same rule to every point of an object. The whole object turns and moves. Its shape stays the same.
𝟮. 𝗧𝗵𝗶𝘀 𝗶𝘀 𝘄𝗵𝘆 𝘁𝗵𝗲 𝗺𝗮𝘁𝗿𝗶𝘅 𝗶𝘀 𝗽𝗼𝘄𝗲𝗿𝗳𝘂𝗹.
A computer stores geometry as coordinates.
Matrices provide a common way to:
• Move and rotate objects.
• Change the camera view.
• Combine several transformations into one.
A GPU can process these calculations quickly for many points.
𝟯. 𝗖𝗔𝗗, 𝘀𝗶𝗺𝘂𝗹𝗮𝘁𝗶𝗼𝗻 𝗮𝗻𝗱 𝗴𝗮𝗺𝗲𝘀 𝘀𝗵𝗮𝗿𝗲 𝘁𝗵𝗶𝘀 𝗳𝗼𝘂𝗻𝗱𝗮𝘁𝗶𝗼𝗻.
These ideas were used in CAD and simulation long before modern 3D games.
The game industry helped bring fast 3D graphics to everyday computers.
Structural software also benefits from this technology.
𝟰. 𝗬𝗼𝘂 𝗰𝗮𝗻 𝘀𝗲𝗲 𝗶𝘁 𝗶𝗻 𝗦𝗰𝗮𝗳𝗳𝗼𝗹𝗱𝗶𝗻𝗴.
Scaffolding reuses an open-source CAD renderer developed by other contributors.
When you drag the mouse to rotate the view:
• The camera changes.
• Transformation matrices define the new view.
• The renderer draws a new image.
What you see rotating in Scaffolding is this same mathematical principle in action.
𝟱. 𝗧𝗵𝗲 𝘀𝗮𝗺𝗲 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀 𝘄𝗼𝗿𝗸𝘀 𝗶𝗻 𝗖𝗮𝘀𝘁𝗖𝗼𝗻𝘁𝗿𝗼𝗹.
CastControl uses coordinate transformations between local and global systems during geometry correction.
These transformations follow the same rotation and translation principles.
𝗜𝗻 𝗦𝗰𝗮𝗳𝗳𝗼𝗹𝗱𝗶𝗻𝗴, they help us view a structure (𝗦𝘁𝗮𝘆 𝘁𝘂𝗻𝗲𝗱. Scaffolding is launching soon!)
𝗜𝗻 𝗖𝗮𝘀𝘁𝗖𝗼𝗻𝘁𝗿𝗼𝗹, they help us calculate coordinates for segment casting.
Explore CastControl and learn more about our 𝗮𝘂𝘁𝗼𝗺𝗮𝘁𝗲𝗱 𝗴𝗲𝗼𝗺𝗲𝘁𝗿𝘆 𝗰𝗼𝗻𝘁𝗿𝗼𝗹 𝘀𝗲𝗿𝘃𝗶𝗰𝗲𝘀: https://lnkd.in/gFstcRni
P.S. In my view, strong 3D graphics helped shape MIDAS Civil’s success.
At the time, SAP2000’s graphics felt much more basic.
MIDAS made models easier to see, rotate and explore.
That visual appeal could draw students and new engineers into the software.
Established mathematics, used well, can help a program make its mark.
