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FocalPoint, FocalPointX, FocalPointY, FocalPointZ

Focal point of a camera

Value Summary

FocalPointLibrary wrapper for "[FocalPointX, FocalPointY, FocalPointZ]" (3D)List of 2 or 3 expressions, depending on the dimension
FocalPointX, FocalPointY, FocalPointZOptionalMuPAD® expression

Graphics Primitives

ObjectsDefault Values


The attribute FocalPoint refers to the point a camera taking pictures of a 3D scene is aimed at. Its value is a list or vector of coordinates (numerical values or symbolic expressions of an animation parameter).

FocalPointX etc. refer to the single coordinates x etc.

The optical axis of the camera is given by the vector from the camera Position to its FocalPoint.

When creating a camera by

camera := plot::Camera(camera_position, focal_point, opening_angle),

the focal point is the second argument. Internally, this point is stored as the attribute FocalPoint and can be accessed and changed as camera::FocalPoint.

The focal point attributes can be animated.

Of course, the focal point should be set such that the camera points into the direction of the objects that are to be rendered. Typically, for a camera positioned outside the graphical scene, a good focal point is the center of the scene.


Example 1

We define a scene consisting of 4 geometric objects:

b := plot::Box(4..5, -1..1, -1..1, Filled = FALSE, 
               LineColor = RGB::Red):
c1 := plot::Cone(1, [0, 4, 0], [0, 4, 1], Color = RGB::Green):
s := plot::Sphere(1, [-4, 0, 0], Color = RGB::Blue):
c2 := plot::Cone(1, [0, -4, 1], [0, -4, 0], 
                 Color = RGB::Orange):

We use a small black object to mark the point (0, 0, 0.5), where we wish to place an animated camera:

cameraposition := plot::Group3d(
      plot::Box(-0.1..0.1, -0.3..0.3, 0.3..0.7,
                Color = RGB::Black),
      plot::Cone(0.1, [0, 0, 0.5], 0.3, [0.5, 0, 0.5],
                 Color = RGB::DarkGrey)):
plot(b, c1, s, c2, cameraposition)

When defining the camera, the second argument is the FocalPoint. In this case, it is animated: The camera is to turn around the z-axis.

camera := plot::Camera([0, 0, 0.5], [4*cos(a), 4*sin(a), 0], 
                      PI/4, a = 0..2*PI):

We insert the animated camera:

plot(b, c1, s, c2, camera)

delete b, c1, s, c2, cameraposition, camera:

Example 2

We define a function and a camera with an animated focal point:

f := plot::Function3d(sin(x^2-y^2), x = -2..2, y = -2..2,
                      Submesh = [2, 2]):
camera := plot::Camera([3, 3, 3], [sin(a), cos(a), 0], 
                       PI/6, a = 0..2*PI):
plot(f, camera)

delete f, camera:
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