Geometry 3D Lab
Explore points, lines, planes and spheres with distances, angles and intersections in 3D coordinates.
Explore the lab
What you can explore
- Points and distances
Move A and B to inspect their distance and midpoint in three-dimensional coordinates.
- Lines and planes
Edit a line direction and plane normal to inspect their angle and line–plane intersection.
- Spatial relationships
Adjust the plane and sphere, then show guides to locate the point-to-plane perpendicular and visible objects.
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The model
Formula and underlying model
d(A,B) = √((Bx−Ax)² + (By−Ay)² + (Bz−Az)²); M = (A+B)/2
Plane: n·X + c = 0; d(P,plane) = |n·P+c|/|n|- A, B, P, X
- Points or position coordinates (abstract length units)
- M
- Midpoint between A and B (abstract length units)
- n, c
- Plane normal and plane constant (coordinate-dependent)
- d
- Distance between points or from point to plane (abstract length units)
Lines are infinite, not rays. The angle result compares line direction with plane normal. Parallel and coplanar lines have special intersection results; zero normals/directions are invalid.
The experiment
How it works
Place the objects
Set point coordinates, line point/direction, plane normal/constant and sphere center/radius.
Choose a relationship
Select distance, midpoint, angle, point-to-plane distance or line–plane intersection.
Inspect the geometry
Orbit the view and compare guides with the numerical result.
Learning outcomes
What you’ll learn
- Relate 3D coordinates to distance and midpoint.
- Interpret plane normals and point-to-plane distance.
- Distinguish intersecting, parallel and coplanar line–plane cases.
Ready to experiment?
Explore Geometry 3D interactively
Open the lab, adjust the parameters, and see the results change in real time.