CPSC 427 Video Game Programming

Helge Rhodin CPSC 427 Video Game Programming

Transformations for Skeleton Kinematics

1 © Alla Sheffer, Helge Rhodin Recap: Fun to play?

https://www.androidauthority.com/level-design-mobile-games-developers- make-games-fun-661877/ 2 © Alla Sheffer, Helge Rhodin Recap: Indirect relationships Value of a piece • It is not possible to get a knight for 3 pawns • But one can ‘trade’ pieces • A currency

How to determine the value? • Ask the users • Auction house

3 © Alla Sheffer, Helge Rhodin Recap: Relationships • Linear relations • Exponential relations • Triangular relationship • 1, 3, 6, 10, 15, 21, 28, …

• The difference increases linearly • The function has quadratic complexity

• Periodic relations

4 © Alla Sheffer, Helge Rhodin Asymptotic analysis? • Linear * linear? • Linear + linear? • Linear + exponential? • Linear * exponential?

5 © Alla Sheffer, Helge Rhodin Numerical Methods - Optimization • Iterative optimizers • Single variable? Exponential Target function • Multiple variables? Linear approx. • Gradient descent?

Constant approx.

Lecture 14: https://youtu.be/ZNsNZOnrM50 • Balancing demo starts at 1h20 • Optimizer used at ~ 1h30

6 © Alla Sheffer, Helge Rhodin Difficulties: • Placement of towers changes the time damage is dealt

• Path of enemies can be hindered to increase time

➢ Measure during playtest ➢ cross-play

• Some enemies are resistant to fire/magic/…? • kind of a periodic feature

7 © Alla Sheffer, Helge Rhodin Counter Measures • Transitive Mechanics • Repair costs • Consumables (food, potions, …) • Tax

8 © Alla Sheffer, Helge Rhodin A/B Testing Testing two variants of your game (with and w/o a feature) • randomized participants (same pool) • with respect to a measurable objective (e.g., clicks on website)

Related to • two-sample hypothesis testing • Clinical tests, e.g., testing of a COVID-19 vaccine • Placebo effect 9 https://www.optimizely.com/optimization-glossary/ab-testing/ © Alla Sheffer, Helge Rhodin Logistics

10 © Alla Sheffer, Helge Rhodin M4 updated requirement User study

Carefully balance one aspect of your game (e.g., movement-speed, health points, strength, bonus,…). • Report on the theoretical analysis • Change log with testing

11 © Alla Sheffer, Helge Rhodin M4 Advanced shaders? • Use ShaderToy.com

• Demo in Lecture 4 https://youtu.be/S97-fYMv4Xk 45 minute mark

12 © Alla Sheffer, Helge Rhodin Upcoming lectures: Tuesday: • Working in teams • Supported by TA Thursday: • Last formal lecture: • Skeleton Animation continued • Summary and Outlook Tuesday (April 13.): • M4 grading with TAs Monday (April 19.): • Final cross play, including industry jury and awards 13 © Alla Sheffer, Helge Rhodin Final cross play

Room Purpose Timeline: 1 Team 1 – open cross-play 7 – 8 pm: scheduled (10 minutes) cross play 2 Team 2 – open cross-play 7 – 8:30 pm: open cross play (those not with jury) … … 8 – 8:30 pm: jury votes, student votes are counted 8:30 – 9 pm: awards! 12 Team 12 – open cross-play 13 Jury 1 (Skybox) – scheduled 10 min slots Communication: 14 Jury 2 (EA) – scheduled 10 min slots On Slack to reach beyond zoom rooms … … • OK to include jury? 20 Overflow – breakout for open cross-play 21 Overflow – breakout for open cross-play Presence: … … • Mandatory!

14 © Alla Sheffer, Helge Rhodin Today Becoming an expert on transformation • Mental picture • Math • Practical examples

Composite transformations • Articulated skeleton motion • Skeleton animation

15 © Alla Sheffer, Helge Rhodin Recap: Transformations Lecture 3, 20 minute mark • https://youtu.be/l9xQUxJT7fg

16 © Alla Sheffer, Helge Rhodin From local object to camera coordinates

Camera Camera World World coordinates coordinates coordinates coordinates y y x x

x x y y

object -> world world -> camera object -> camera

transform projection projection * transform

17 © Alla Sheffer, Helge Rhodin Recap: GLSL Vertex shader

The OpenGL Shading Language (GLSL) • Syntax similar to the C programming language • Build-in vector operations x and y coordinates • functionality as the GLM library our assignment template uses of a vec2, vec3 or vec4 world object void main() -> camera -> world { // Transforming The Vertex vec3 out_pos = projection * transform * vec3(in_pos.xy, 1.0); gl_Position = vec4(out_pos.xy, in_pos.z, 1.0); } float vector of 3 (vec3) and 4 (vec4) floats (32 bit)

18 © Alla Sheffer, Helge Rhodin Affine transformations • Linear transformations + translations • Can be expressed as 2x2 matrix + 2 vector • E.g. scale+ translation:

 x' x'2 02 00xx Ttxx     =   +    y'=y'0 20 02yy +Tty           z'  0 0 1  z   0 

Adding a third coordinate  x'  x'2 02 00  0x xt  t   x' x'2 02 00xx Tt            x   x     =   +  xx  y' =y'0 =20 02 0y + yt + t y' = 0 2 0  y +Tt            y   y    y' 0 2y  yy                         z'   z'0 00 10  1z  z0   0   z'  0 0 1  z   0   x' 2 0 0  x  t         x   y' = 0 2 0  y + ty           z'  0 0 1  z   0  Affine transformations are now linear • one 3x3 matrix can express: 2D rotation, scale, shear, and translation

• Examples?

• Later: Inverse transformations

21 © Alla Sheffer, Helge Rhodin Parallax scrolling background Further objects • are smaller • move slower Multiple layers!

Weak perspective projection • Approximates perspective projection

22 © Alla Sheffer, Helge Rhodin Parallax scrolling background Ingredients: • Multiple layers • One sprite per layer • One transformation per layer • Scale down with distance • Move inversely proportional to the distance  x' 2 0x'0 2x 0 t0  x  t           x     x   y' = 0 2y'0= 0y2+ t0y  y + ty                 z'  0 0z' 1 0z 0  01  z   0 

23 © Alla Sheffer, Helge Rhodin 24 © Alla Sheffer, Helge Rhodin TRANSFORMATION COMPOSITION

 p   x  • What operation rotates XY by  around P = ?   py 

P P

 p   x  • What operation rotates XY by  around P = ?  py • Answer:   • Translate P to origin

P P

 p  • What operation rotates XY by 휃 < 0 around P = ? x   p  • Answer:  y  • Translate P to origin • Rotate around origin by  • Translate back

P P

( p , p ) (− px ,− p y ) T x y RT (V ) 1 0 p cos − sin  01 0 − p v  x x  x  = 0 1 p sin  cos 00 1 − p  v  y   y  y    0 0 1  0 0 10 0 1  1 