Simple representation of approximate area covered by an object
Always completely contains the object
Typically a box or a circle/sphere
To determine if a point (x,y) is inside a bounding box:
(x >= minX) and (x <= maxX) and
(y >= minY) and (y <= maxY) and
(z >= minZ) and (z <= maxZ)
To compute a bounding box of an object, assuming its vertices are contained in the list obj.vertices:
minX = obj.vertices[0][0]
maxX = obj.vertices[0][0]
minY = obj.vertices[0][1]
maxY = obj.vertices[0][1]
minZ = obj.vertices[0][2]
maxZ = obj.vertices[0][2]
for v in obj.vertices:
if minX > v[0]:
minX = v[0]
elif maxX < v[0]:
maxX = v[0]
if minY > v[1]:
minY = v[1]
elif maxY < v[1]:
maxY = v[1]
if minZ > v[2]:
minZ = v[2]
elif maxZ < v[2]:
maxZ = v[2]
To determine if a point (x,y,z) is inside a bounding sphere:
distance(center, (x,y,z)) <= radius
To compute a bounding sphere, find a center, and then the most distant vertex:
xsum,ysum,zsum = 0,0,0
for v in obj.vertices:
xsum += v[0]
ysum += v[1]
zsum += v[2]
center = [ xsum / len(obj.vertices) , ysum / len(obj.vertices), zsum / len(obj.vertices) ]
radius = 0
for v in obj.vertices:
d = distance(v, center)
if d > radius:
radius = d
Note that this computes a bounding sphere, but generally not the smallest bounding sphere - that is a much more complex problem.
Compute the overlap of two boxes - the region of points which are contained in both boxes. If an overlap exists, they collide.
OR
If the boxes don't overlap, then box1 must be entirely to the left of box2, or box1 is to the right of box2, or box1 is above box2, etc. For box1 to be left of box2, it's minX will be greater than box2's maxX; similar tests apply for the other 5 cases. Testing for overlap is then the negation of this.
def BoxCollidesWithBox(box1, box2):
return (box1.minX <= box2.maxX) and
(box1.maxX >= box2.minX) and
(box1.minY <= box2.maxY) and
(box1.maxY >= box2.minY) and
(box1.minZ <= box2.maxZ) and
(box1.maxZ >= box2.minZ)
Compute distance between the centers of the two spheres. If it's less than the sum of the radii, then there exist points that lie within both spheres -> the spheres overlap.
def SphereCollidesWithSphere(s1, s2):
d = s1.center.distanceSquared(s2.center)
rsum = s1.radius + s2.radius
return (d <= rsum*rsum)
Change in response to users' actions
Lets users know that they're interacting
Immediate, simple response often useful
Can be visual, auditory, haptic
Delay between an action and its result
Humans very aware of latency > ~ 100 milliseconds
Many delays inherent in different stages of hardware/software
"End-to-end" latency = total delay
Long latency slows up user
Irregular latency even worse
Latency is distinct from update speed
Measure of how many distinct values a device can report
On/off switch = 1 bit resolution
"Non-analog" joystick = 3 values (+1, 0, -1) for X and for Y
8 bit resolution joystick = 256 possible values for X and for Y
16 bit resolution joystick = 65536 possible values for X and for Y
Signal = the information we want to communicate to the computer (e.g. button state, pointer position)
Noise = variations in the signal, outside of our control
Examples:
Applications may need to allow for noise in input data
From human movement research - Paul Fitts, 1954
Predicts time needed to move from a starting position to a target - e.g. to point at something
D = distance to target
W = width of target
