Graphics - Euler Angle

2

to orient a vector rooted at the origin, it only requires _____ angles

3

to orient a rigid body in a fixed coordinate system requires ____ angles

x, roll

Φ (phi) represents the rotation about the __ __axis and is known as__ __

also referred to as the bank angle

<answer>,<answer>

y, pitch

θ (phi) represents the rotation about the __ __axis and is known as__ __

also referred to as the elevation angle

<answer>,<answer>

z, Yaw

Ψ (phi) represents the rotation about the __ __axis and is known as__ __

also referred to as the bearing angle

<answer>,<answer>

red, green, blue

what is the order of blue, red, and green when matching them to the order x,y, and z

T

T/F We can use the homogenous rotation coordinates to represent Euler angle transform

point

we only need 2 angles to orient a vector because we are identifying a direction and not a specific _____ in 3D space

Tait-Bryan

the ________ orders the angle transforms as

x-y-z x-z-y y-z-x z-x-y z-y-x

Proper Euler

the ______ orders the angle transforms as

z-x-z z-y-z y-x-y y-z-y x-y-x x-z-x

F

T/F all of the Euler angle transforms are not affine transforms

center

TRT is the matrix multiplication order that will rotate a matrix about its _______

point’s coordinates

You need the Euler angles, the center of the object, and the (two words) to compute the Euler Angle Transform

step one

(two words) of Euler Angle Transform must be performed any time any of the angles change

step two

(two words) of Euler Angle Transform must be performed any time Step One is performed or when any of tx, ty, tz values change. The objects center changes whenever the object is translated to a new position

step three

(two words) has to be performed for every point that is to be transformed any time Step One or Step Two is performed. All points have to be transformed every time the object is drawn

center

the ______ of an object can be found by averaging the max and min of each the x, y, and z values, resulting the in the x,y, and z coordinates of the *(same word)*