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23 + 11 years ago*

Coming back to this, and I think I got it working fairly well in Unity, though I made a separate ToVector method that doesn't scale by the Cos of the pitch (so the vector doesn't shrink and speed doesn't lessen) and some other changes. I'm just surprised and happy I seem to have gotten it working tbh. public VectorNew ToVectorNoCosPitch() { VectorNew result; if (pitch < 0) pitch = 0; result.x = Mathf.Cos(yaw + 90 * Mathf.Deg2Rad);// * Mathf.Cos(pitch); result.y = -Mathf.Sin(pitch); result.z = Mathf.Sin(yaw + 90 * Mathf.Deg2Rad);// * Mathf.Cos(pitch); return result; } public void FixedUpdate() { vecMovement.z = Maths.Approach(veloMovementGoal.z, vecMovement.z, Time.deltaTime * 40); vecMovement.x = Maths.Approach(veloMovementGoal.x, vecMovement.x, Time.deltaTime * 40); //vid 14, Cross Product vecForward = camEulerAngle.ToVectorNoCosPitch(); vecForward.y = 0; vecForward.Normalized(); Debug.Log($"vecForward: {vecForward}"); Debug.Log($"vecForward length: {vecForward.Length()}"); VectorNew vecRight = VectorNew.CrossProduct(new VectorNew(0, 1, 0), vecForward); //VectorNew vecVelo = vecForward * vecMovement.z + vecRight * vecMovement.x; Debug.DrawRay(rbPlayer.transform.position, new Vector3(vecRight.x, vecRight.y, vecRight.z), Color.yellow); rbVeloForward = new Vector3(vecForward.x, 0, vecForward.z) * vecMovement.z; rbVeloRight = new Vector3(vecRight.x, 0, vecRight.z) * vecMovement.x; Debug.Log($"forward: {rbVeloForward}, right: {rbVeloRight}, vecForward: {vecForward}"); rbPlayer.position += (rbVeloForward+rbVeloRight) * Time.deltaTime; }

For anyone watching this, avoid naming your variables 'x' and 'y' at all costs. Because you end up naming other variables 'X' and 'Y' and so on. And then you read the code in 3 months and understand nothing. Just create an object, give it a real name, and put the x and y inside as keys.

Ultra super amazing very cool ❤️‍🔥🔥

The best series ever!! Great!

This is pure gold man, I love this so much! I can't wait to find out how to calculate x and y values in order to rotate the vector towards something

Thanks! This puts the useless math I learned in high school into perspective. That's what I always lacked in math class. Gonna use these videos to learn more about both math and game dev.

Auto subscribe bro, Thankyou,

great video! You have good teaching skills

all i have written code in is c and java (tf is cpp, man its getting over my head, only at some places) iget the concept but not the code

Great series. from watching these, it demystified matrices, and it informed me that I was doing matrix (like) math, but using vectors instead [scaling basis vectors then adding them together]. there is one thing that wasn't clear. right after this (or mid) series I was able to start using matrices for things (not really related to your video, because of my understanding), but I realized I don't know how the math works with the translation so much and what it does to the basis vectors during multiplication etc. do you have any resources on that? you explain very well the basis vector thing, buy you kind glosed over the translation part of the matrix.

Although I left C++ for C, two years ago, I'm so fortunate, that can understand enough C++, so I can benefit from this fantastic video series. Your way of teaching and your pedagogical approach, is an example to follow for other RUclipsr's. You are using the full screen and don't have irrelevant information and very important, no disturbing background music. I'm using Raylib graphics, that also are made for teaching and for games.

Where can i find more material about this? I'm saying books or a webpage or something like this?

thank you so much for this amazing series

11 years old and still useful thank you ❤

This was really encouraging, thank you

5:50 Why is it so bright

Hey, what if I have 1000 object, and for each I need to check its state first, then do stuff for picked one depending on state, check collisions etc before I move to next character? Is there a way to do it with this approach? And what if I need to compare a value of object index 3 with object index 10 for example? I'm having hard time imagining this.

Here are my Unity / C# scripts (in separate comments), if it helps somebody. (VectorNew is the Vector class I created for this series. Vector3 is Unity's regular vector class.) using System.Collections; using System.Collections.Generic; using UnityEngine; //(started in Video 12) public class Game : MonoBehaviour { [SerializeField] float maxSpeedAbs; float minSpeedAbs = 0; [SerializeField] Rigidbody rbPlayer; [SerializeField] Camera cam; public VectorNew veloGoal; public VectorNew veloCurrent; Vector3 rbVelo; EulerAngle camEulerAngle; VectorNew camVector; private void Start() { camEulerAngle = new EulerAngle(); camEulerAngle.pitch = 0.6f; //radian amount to start with looking slightly down at an angle } void KeyRelease(float minSpeed) { if (Input.GetKeyUp("w")) veloGoal.z = minSpeed; if (Input.GetKeyUp("s")) veloGoal.z = minSpeed; if (Input.GetKeyUp("d")) veloGoal.x = minSpeed; if (Input.GetKeyUp("a")) veloGoal.x = minSpeed; } void KeyPress(float maxSpeed) { if (Input.GetKey("w")) veloGoal.z = maxSpeed; if (Input.GetKey("s")) veloGoal.z = -maxSpeed; if (Input.GetKey("d")) veloGoal.x = maxSpeed; if (Input.GetKey("a")) veloGoal.x = -maxSpeed; } float sensitivity = 0.1f; void MouseMotion() { float mouseX = Input.GetAxis("Mouse X"); float mouseY = Input.GetAxis("Mouse Y"); camEulerAngle.pitch += mouseY * sensitivity; camEulerAngle.yaw += mouseX * sensitivity; camEulerAngle.Normalize(); } public void Update() { KeyPress(maxSpeedAbs); KeyRelease(minSpeedAbs); MouseMotion(); } public void FixedUpdate() { veloCurrent.z = Maths.Approach(veloGoal.z, veloCurrent.z, Time.deltaTime * 40); veloCurrent.x = Maths.Approach(veloGoal.x, veloCurrent.x, Time.deltaTime * 40); if (veloCurrent.x > 0) { Debug.Log($"VeloCurrent.x: {veloCurrent.x}"); Debug.Log($"VeloCurrent.x * dt: {veloCurrent.x * Time.deltaTime}"); } //(set the VectorNew into a Vector3) rbVelo = new Vector3(veloCurrent.x, 0, veloCurrent.z); rbPlayer.position += rbVelo * Time.deltaTime; } private void LateUpdate() { VectorNew cEA = camEulerAngle.ToVector(); Vector3 camPos = new Vector3(cEA.x, cEA.y, cEA.z); cam.transform.position = rbPlayer.gameObject.transform.position - camPos * 5f; Vector3 dir = rbPlayer.gameObject.transform.position - cam.transform.position; Debug.DrawRay(cam.transform.position, dir, Color.red); cam.transform.rotation = Quaternion.LookRotation(dir, Vector3.up); } }

This is my 3rd time coming back to this video, probably been somewhere north of 6 months since the first time... I just successfully calculated the reflect vector in my game. Once I inverted the vector and thought about it from the hit location it all made so much more sense.

still watching this neve die

5 years later on a different account and going back through olde vids, here's another Unity/C# version I came up with (still took me embarrassingly long to figure it out, but oh well :P) : public class Maths : MonoBehaviour { public static float Approach(float goal, float current, float dt) { //how far left to we have to go before we get to our goal float difference = goal - current; Debug.Log($"Goal: {goal}, Current: {current}, Diff: {difference}, DT: {dt}"); //--- interpolate up or down //if dt is not enough to take us to our goal if (difference > dt) { Debug.Log($"diff > dt. return {current + dt}"); return current + dt; //return one step further to our goal } /*edge case: if goal is lower than current (interpolating in the downward direction / value is getting lower), then difference will be negative*/ if (difference < -dt) { Debug.Log($"diff < -dt. return {current - dt}"); return current - dt; } //otherwise, if in range of goal, return goal return goal; } } public class Game : MonoBehaviour { [SerializeField] float maxSpeedAbs; float minSpeedAbs = 0; [SerializeField] Rigidbody rbPlayer; public VectorNew veloGoal;/ public VectorNew veloCurrent; Vector3 rbVelo; public void KeyRelease(float minSpeed) { if (Input.GetKeyUp("w")) veloGoal.z = minSpeed; if (Input.GetKeyUp("s")) veloGoal.z = minSpeed; if (Input.GetKeyUp("d")) veloGoal.x = minSpeed; if (Input.GetKeyUp("a")) veloGoal.x = minSpeed; } public void KeyPress(float maxSpeed) { if (Input.GetKey("w")) veloGoal.z = maxSpeed; if (Input.GetKey("s")) veloGoal.z = -maxSpeed; if (Input.GetKey("d")) veloGoal.x = maxSpeed; if (Input.GetKey("a")) veloGoal.x = -maxSpeed; } public void Update() { KeyPress(maxSpeedAbs); KeyRelease(minSpeedAbs); } public void FixedUpdate() { veloCurrent.z = Maths.Approach(veloGoal.z, veloCurrent.z, Time.deltaTime * 40); veloCurrent.x = Maths.Approach(veloGoal.x, veloCurrent.x, Time.deltaTime * 40); if (veloCurrent.x > 0) { Debug.Log($"VeloCurrent.x: {veloCurrent.x}"); Debug.Log($"VeloCurrent.x * dt: {veloCurrent.x * Time.deltaTime}"); } //(set the VectorNew into a Vector3) rbVelo = new Vector3(veloCurrent.x, 0, veloCurrent.z); rbPlayer.position += rbVelo * Time.deltaTime; } }

This is a tutorial that never expires Thanks 🥰

At 1:25 you say it's h times the vector between those positions, but pretty sure it's the vector between those two positions divided by h (what was written is that vector is equal to the velocity multiplied by h which is true, just misspoke I guess).

thanks buddy! it helped me a lot

Ultra mega cool awesome amazing super helpful!!❤

Super, amazing, literally the best!!!❤

Just started learning game dev and was strugling with the vector and matrix math, almost all content out there is too direct no explanation, or pure math.... yours is really good, and helped me a lot.

I’d love to see more analyses

Ultra top amazing!! The author is just great😎✨

Another trick is when you are using integer values for x and y and then you don't have to calculate every time x*x and y*y, but you can create in the beginning field(lookup table) of all numbers that x and y can have. Let's say x can have 0-65535 values an y can have 0-65535 values. Then you can create one field that is storing 65536 values of number*number values to lookup instead of doing calculations all over the time when these values are needed.

I came looking for copper and i found GOLD !

It makes so much sense now. Thanks.

ultra top!! Cool!

ultra mega awesome!! thank you very much!

super ultra amazing!!!

amazing ultra cool!!!

Super great amazing!! Thank you!!

Ultra super amazing thank you very much !!!❤

Amazing ultra cool thank you!!!❤

Amazing super cool!!

I made a test version in Unity / C# using a Coroutine/IEnumerator and it worked okay but I couldn't figure out how to make the character end at the correct size, so I went ahead and reworked your version, and it seems to be working as intended! I'm using Mario sprite and I just have him start resizing when the spacebar is pressed. [SerializeField] Transform tran_Mario; // Update is called once per frame void Update() { Update_Vid102(); } bool grow = false; void Update_Vid102() { if (Input.GetButtonUp("Jump")) { grow = true; } if (grow) Grow_Vid102(); } bool gotStartTime; float startTime; Vector3 marioStartSize; void Grow_Vid102() { if (!gotStartTime) { startTime = Time.time; marioStartSize = tran_Mario.localScale; gotStartTime = true; } float lerp = Maths.RemapClamp(Time.time, startTime, startTime + 2, 0, 1); lerp = Maths.CubicInterpolation(lerp); float size = Maths.RemapClamp(lerp, 0, 1, marioStartSize.x, 5); tran_Mario.localScale = Vector3(dot)one * size; }

1:49 isn't the force of gravity on earth 9.8 m/s²?

The deep space monster in Kerbal Space Program is known as The Kraken and has no corporeal form. It lurks in the space between time steps and feeds on numerical instabilities.

Great video! Theres just one thing I dont understand. How do you obtain an elliptical orbit in the end if the acceleration stays the same? Or does the acceleration change everytime there is a new position?

Thank you so much, I'm making my first map and everyone online just said to "optimize the map" with literally no explanation how. I just assumed every block started as a func_detail.

How do you choose the tangents for the triangular mesh btw?

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really like the videos so far, is it the full completed list or is it still being added to ?