Lernkartei Interactive Computer Graphics (Seite 6 von 7)

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Erstellt / Aktualisiert	27.07.2022 / 31.07.2022
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Which facts below about pinhole cameras are true?

Human eyes are approximated in computer graphics as pinhole cameras.

The rendering camera is approximated in computer graphics as pinhole cameras.

They don't have a focal point.

The distance from the apparatus to the image plane defines the field of view.

The image to be taken is flipped on both axis (x and y)

Which of the steps below are related to clipping?

The normalization matrix has to be applied

The points have to be projected on the xy plane.

The view volume has to be translated & rotated and scaled into an Axis Aligned Bounding Box

In which direction is the camera looking, using world coordinates, aka. being in the World Space?

It is looking in the negative z direction.

It is dependant on the position of the camera relative to the objects.

It is looking in the positive x direction.

Switching between the left and right handed Coordinate Systems can be done by multiplying the z component with -1. What is the effect, if you use this matrix instead:

1 0 0 0
0 -1 0 0
0 0 1 0
0 0 0 1

Nothing. Flipping one axis changes the handiness.

The rendered image is flipped.

The camera is facing the wrong direction and orientation.

Flipping the z axis is the only option to switch between RH and LH cosy.

What happens to the center of projection when we set the near and far plane to the same geometry, i.e. same width and hight?

The perspective transformation matrix cannot be computed.

The center of projection is infinitely far away.

There is no center of projection.

This is the definition of orthographic projection.

When is it efficiently possible to perform clipping in the world coordinate system when using perspective rendering?

If the camera is looking one base vector, like the negative z direction

It is never practically efficient to perform clipping in the world space.

If the camera is facing the negative z direction, the field of view is 2π. and being in the origin.

If one renders only one pixel.

Why is the perspective projection matrix not affine?

Moving the frustum to the origin and flipping the z value flips the angle α between two intersecting lines by 180° - α.

The camera might be rotated and the scene has to be rotated.

The shape of the frustum becomes a cube and contained objects alter accordingly.

What is z fighting?

After a non linear transformation of the z value, objects near to the far plane suffer from a lag of bits to represent the difference between them.

Can z fighting occur in parallel / orthographic projection as well?

Yes

No

Depends on the hardware

What happens to two objects relatively close to the camera if the distance of the far plane increases?

They appear to be further away of each other.

They appear to be closer together of each other.

Nothing.

How can we add the lense distortion effect of barrel distortion?

Scale the pixels with the distance to the center

Moving the camera backwards along the z axis for by the distance from the center in x direction.

Averaging the pixel values by the 8 neighbor pixels it.

Which of the following statements about the two image synthesize approaches are correct?

Ray tracing follows objects from 2D to 3D.

Rasterization operates in object and screen space.

Ray tracing is backwards rendering.

Rasterization exploits coherence more easily.

In what order does object referencing happen in a Model-World Transformationi (Rasterization)?

View Space → Model Space → World Space

View Space → World Space → Model Space

World Space → View Space → Model Space

World Space → Model Space → View Space

Model Space → World Space → View Space

Light-Material Interactions (and hence determining color shades) is ...

... done per fragment in the lighting stage.

... done per object after primitve assembly.

... done per fragment during the shading stage.

... done per vertex during the lighting stage.

Visibility resolution ...

... is implicit for ray tracing.

... has to be performed explicitly during rasterization.

... is the last per fragment operation before frame buffer is written during rasterization.

Following structure could be a ...

struct guess_me {
int x, y;
float depth;
int r, g, b, a;
}

vertex

pixel

primitve

object

fragment

Let

T: translation to origin of canonical view volume.
S: scale to fit edges to edges of canonical cube.
N: z-mapping to reflect depth ordering.

What are correct assertions?

A perspective normalization matrix would be STN.

S is the same for the parallel and perspective cases.

A parallel normalization matrix would be SN.

What are correct assertions?

Using two on-axis perspective projections is the correct way to generate stereo images.

Using two off-axis perspective projections will not cause any ergonomic problems.

Screen-based stereoscopy with current technology is sub-optimal.

What is the reason, one makes use of the Δt approach in real time computer graphics?

To cope with inconsistent frame rates.

To interpolate movement, i.e. to describe motion between values of 0.0 and 1.0 on each axis and angle.

To make the render loop and animation loop independent.

To deal with different monitor refresh rates.

In which of the cases below is it necessary/advisable to use key frames?

Animation of a baseball player hitting a ball, which follows a parabola curve.

Making a cube bounce animation by compressing along z and expanding along x & y.

Animating non player competing cars in a race car simulation.

Animating characters and their facial expressions in a computer generated movie.

Animating interactive elements like buttons on websites.

Which order of operations does make sense for the use in interactive realtime computer graphics?

Scene Render, Display Image, Evaluation of User Input, Animation

Display Image, Evaluation of User Input, Scene Render, Animation

Evaluation of User Input, Animation, Scene Render, Display Image

Evaluation of User Input, Scene Render, Display Image, Animation

Scene Render, Display Image, Animation, Evaluation of User Input

In computer games Gizmos are defined locations of interest.
They do not have a visual appearance to the player, but should be visible to the game designer.
Using a scene graph node for the gizmo, how can we achieve the desired behavior?

Not assigning a geometry to the node.

Tell the renderer to ignore gizmo nodes for the player

Setting the alpha channel of the object to 255, i.e. transparent.

fₐ is a time-dependent animation function. What is a requirement for smooth kinematics?

fₐ is D₃ continuous

fₐ is C₂ continuous

fₐ is A₁ continuous

fₐ is G₄ continuous

Why is the simulation time advanced by variable Δt increments instead of fixed increments?

Frame rates might not be constant

Animation functions can not be sampled at fixed intervals.

To meet frame boundaries.

Check the correct statements regarding the local clock of an animation clip.

There is only one local clock.

The local clock time index is set to zero on animation start.

Each clip records the local time at which it started playing.

Which is the correct formula for linear interpolation with parameter β?

(1 - β)pₐ + βpₑ

(1 / β)pₐ + βpₑ

(1 - β)pₐ + (1 / (1 - β))pₑ

What is the Gimbal Lock?

The loss of one degree of freedom when expressing certain rotations with euler angles.

The different possible permutations of ordering euler angles.

An arbitrary rotation around the negative z-axis.

A special case that makes it impossible to compute the euler angles from the transformation matrix.

Why is the atan2 important to computer graphics?

The atan function is not defined at kπ. atan2 is its substitute.

To convert between Euler angles and transformation matrices.

It is not special. We could replace it by atan(y/x).

Which complex number is equal to eⁱ⁽^π/2)?

1

i

-1

-i

What is the formula for spherical linear interpolation?

(sin(Φ(1 - t)) / sinΦ) · q + (sin(Φt) / sinΦ) · r

(cos(Φ(1 - t)) / cosΦ) · q + (sin(Φ) / sinΦt) · r

(sinΦ / sin(Φ(1 - t))) · q + (cos(Φt) / cosΦ) · r

(sinΦ(1 - t) / cos(Φ(1 - t))) · q + (sin(Φt) / cosΦ) · r

What is the result of a spherical linear interpolation between quaternions q and r slerp(q, r, t) with parameter t = 0.

r

q * r

q

What are the consequences of the frame time sequences of two processes with un-synced steps of variable duration?

In interactive computer animation always apply the Δt principle.

The process generating the top sequence can use a fixed Δt.

For each frame calculate change Δt as its timestamp minus the timestamp of the preceding frame.

Which assertions are correct when it comes to value interpolation?

Might need to consider Steven’s Power Law (Weber-Fechner Law)

The value function has to be continous.

Doesn’t need to respect ψ(I) = kIᵃ.

Linear interpolation is always ok.

What are correct assertions for animating Rotation R using a sole parameter t as depicted?

a₁₁(t) a₁₂(t) a₁₃(t) 0
a₂₁(t) a₂₂(t) a₂₃(t) 0
a₃₁(t) a₃₂(t) a₃₃(t) 0
0 0 0 1

Upper left 3x3 matrix A will stay orthonormal.

Parameter t has to be set according to the Δt calculation.

Components to change are not independent of each other.

Consequences of parameterized Euler angles are?

Interpolating Euler angles always works.

Any rotation (or sequence of rotations) about a point is equivalent to a single rotation about some axis through that point.

Rotation interpolation is solved for good.

Consequences of parameterized Euler angles are?

Interpolating Euler angles always works.

Any rotation (or sequence of rotations) about a point is equivalent to a single rotation about some axis through that point.

Rotation interpolation is solved for good.

Rotating a vector r by displacement (δ, n) is the same as ...

... lifting it into quaternion space as unit quaternion (cos (δ/2), sin (δ/2)n) ...

... and performing q()q⁻¹ on quaternation (0, r) where ...

... orientation can be manipulated using parameterized quaternions cos (δ/2) sin (δ/2)nx, sin (δ/2) ny, sin (δ/2) nz ...

... and where the results can not be translated to matrix form and vice versa.

Observations of Animations are ...

slerp moves in constant speed.

lerp demonstrates the distortion of a rotating point when quaternions are not normalized.

naive nlerp travels on an arc.

naive nlerp minimizes torque and preserves velocity.

Which calculation does this matrix represent?

1 0 0 a
0 1 0 b
0 0 1 c
0 0 0 1

(x, y, z) ⟼ (x + a, y + b, z + c)

(x, y, z) ⟼ (x * a, y * b, z * c)

(x, y, z) ⟼ (a, b, c)

What is the reason for the skinning artifacts?

What does it have to do with the blended matrix T := ∑ₓwᵢₓTₓ ?

T is not symmetric anymore.

T is not orthogonal anymore.

T is not rigid motion anymore.

T is not invertible anymore.

Interactive Computer Graphics

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