Catching Ball
Running to catch a ball in flight
This model was inspired by this illuminating video (which highlights just how much we can seek to 'use math' in testing and assessing models etc)
It is suggested going through the full video on this fascinating area of research but (if pressed for time) the example used begins at time stamp 5:27
Youtube Google Techtalk
"Human Perception Viewed as a Phenotypic Expression"
Google Tech Talk
October 26, 2011
Presented by Dennis Proffitt.
ABSTRACT
"Visual experience relates the optically-specified environment to people's ever-changing purposes and the embodied means by which these purposes are achieved. Depending upon their purpose, people turn themselves into walkers, throwers, graspers, etc., and in so doing, they perceive the world in relation to what they have become. People transform their phenotype to achieve ends and scale their perceptions with that aspect of their phenotype that is relevant for their purposive action. Within near space, apparent distances are scaled with morphology, and in particular, to the extent of an actor's reach. For large environments, such as fields and hills, spatial layout is scaled by changes in physiology -- the bioenergetic costs of walking relative to the bioenergetic resources currently available. When appropriate, behavioral performance scales apparent size; for example, a golf hole looks bigger to golfers when they are putting well. Research findings, conducted in both natural and virtual environments (VR), show that perception is influenced by both manipulations of and individual differences in people's purposive action capabilities."
.
https://www.youtube.com/watch?v=AXGxZUno5qY
My Comment on this
The catcher must run towards the ball while it is in flight in such a way to nulify its apparent transverse motion.
The catcher (who cannot see the ground) will therefore follow a non-linear path in general.
Using vectors and parametization the (constant) horizontal and (accelerating) vertical velocities are isolated.
The apparent transverse velocity (Orange) is separated from the true horizontal (Red) velocity of the ball
The catcher has constant speed (modelled by circle of fixed radius centered on his location)
The Orange vector is translated to the catcher to determine the resultant direction of his total (Purple) velocity.
The assumed overall translation (X to B) is used to generate a Bezier curve with two control points.
The task is therefore to align the curve with the instantaneous direction of the Purple vector throughout.
In this way the path which will nulify the apparent transverse motion of the ball in flight is approximated.