Calculate bounce velocity vector of an object colliding with a moving object












0














I'm making a 2D game where a ball collides with an obstacle.
The ball has a velocity V. When it collides with the obstacle the impact normal vector is iN. I managed to make the ball bounce off the obstacle with the following calculations:




  1. dotProduct = V.x * iN.x + V.y * iN.y

  2. V.x = V.x + 2 * (iN.x * dotProduct)

  3. V.y = V.y + 2 * (iN.y * dotProduct)


So when doing this the ball bounces fine with it's new velocity, now I can't really figure out how to do the same when the obstacle is moving, here is an image to showcase the issue:



enter image description here



In the above picture OV is the velocity of the obstacle, my guess was to add OV to the new velocity but it didn't work quite well, is it a valid solution and the error comes from my program ?






vectors







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    0














    I'm making a 2D game where a ball collides with an obstacle.
    The ball has a velocity V. When it collides with the obstacle the impact normal vector is iN. I managed to make the ball bounce off the obstacle with the following calculations:




    1. dotProduct = V.x * iN.x + V.y * iN.y

    2. V.x = V.x + 2 * (iN.x * dotProduct)

    3. V.y = V.y + 2 * (iN.y * dotProduct)


    So when doing this the ball bounces fine with it's new velocity, now I can't really figure out how to do the same when the obstacle is moving, here is an image to showcase the issue:



    enter image description here



    In the above picture OV is the velocity of the obstacle, my guess was to add OV to the new velocity but it didn't work quite well, is it a valid solution and the error comes from my program ?






    vectors







    share|cite|improve this question

























      0












      0








      0







      I'm making a 2D game where a ball collides with an obstacle.
      The ball has a velocity V. When it collides with the obstacle the impact normal vector is iN. I managed to make the ball bounce off the obstacle with the following calculations:




      1. dotProduct = V.x * iN.x + V.y * iN.y

      2. V.x = V.x + 2 * (iN.x * dotProduct)

      3. V.y = V.y + 2 * (iN.y * dotProduct)


      So when doing this the ball bounces fine with it's new velocity, now I can't really figure out how to do the same when the obstacle is moving, here is an image to showcase the issue:



      enter image description here



      In the above picture OV is the velocity of the obstacle, my guess was to add OV to the new velocity but it didn't work quite well, is it a valid solution and the error comes from my program ?






      vectors







      share|cite|improve this question













      I'm making a 2D game where a ball collides with an obstacle.
      The ball has a velocity V. When it collides with the obstacle the impact normal vector is iN. I managed to make the ball bounce off the obstacle with the following calculations:




      1. dotProduct = V.x * iN.x + V.y * iN.y

      2. V.x = V.x + 2 * (iN.x * dotProduct)

      3. V.y = V.y + 2 * (iN.y * dotProduct)


      So when doing this the ball bounces fine with it's new velocity, now I can't really figure out how to do the same when the obstacle is moving, here is an image to showcase the issue:



      enter image description here



      In the above picture OV is the velocity of the obstacle, my guess was to add OV to the new velocity but it didn't work quite well, is it a valid solution and the error comes from my program ?






      vectors




      vectors






      share|cite|improve this question













      share|cite|improve this question











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      share|cite|improve this question










      asked Jan 4 at 13:29









      MattMatt

      133




      133






















          2 Answers
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          0














          This might be better suited for the physics page. That said you should move to a reference frame where the wall is not moving, do the calculation there, and move back.



          To move to the reference frame where the wall is not moving, we need to subtract away the velocity of the wall for everything. Now the wall's velocity is zero and the ball has a "new" velocity $v' = (v - ov)$. You can then do the calculation as if the wall were stationary, and then move back to the original reference frame (add the velocity of the wall back).



          Note that whey I say add/subtract the velocity of the wall that I mean the velocity as a vector. If your wall is only moving in the $x$ direction, then you only need to adjust the $x$-coordinate.






          share|cite|improve this answer





















          • Thanks it was quite easy to implement in my case and worked really well
            – Matt
            Jan 4 at 15:41



















          0














          If the object moves with velocity $vec v_0$ the ball with velocity $vec v$ and the normal at the impact point is $vec n$ then we have:



          $$
          vec v = vec v_{vec n}+vec v_{Pi}\
          vec v_{Pi} = vec v - vec v_{vec n_1} \
          vec v_r = (vec v-vec v_0)_{Pi}-(vec v-vec v_0)_{vec n}\
          vec v_r = (vec v-vec v_0) -2((vec v-vec v_0).vec v_{vec n})vec v_{vec n}
          $$



          with



          $$
          vec v_{vec n} = left(vec vcdotleft(frac{vec n}{||vec n||}right)right)frac{vec n}{||vec n||}
          $$



          where $vec v_r$ represents the reflected ball velocity after collision



          NOTE



          Here $Pi$ represents the plane passing by the impact point with normal $vec n$



          Attached three cases. Here



          $$
          begin{cases}
          vec v mbox{red}\
          vec v_0 mbox{green}\
          vec n mbox{black}\
          Pi mbox{dashed cyan}\
          vec v_r mbox{blue}
          end{cases}
          $$



          enter image description hereenter image description hereenter image description here






          share|cite|improve this answer























          • What are (v⃗ 0)n⃗ and (v⃗ 0)Π ? This is probably a notation i'm not aware of
            – Matt
            Jan 4 at 15:06










          • @Matt Are the components of $vec v_0$ regarding $vec n$ and $Pi$ They are calculated in the same way as $vec v_{vec n}$ and $vec v_{Pi}$
            – Cesareo
            Jan 4 at 15:10










          • Thank you for the time you took to answer, however your answer didn't really help me, the answer below worked fine.
            – Matt
            Jan 4 at 15:42










          • @Matt Some results attached.
            – Cesareo
            Jan 4 at 19:17











          Your Answer





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          2 Answers
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          2 Answers
          2






          active

          oldest

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          active

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          active

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          0














          This might be better suited for the physics page. That said you should move to a reference frame where the wall is not moving, do the calculation there, and move back.



          To move to the reference frame where the wall is not moving, we need to subtract away the velocity of the wall for everything. Now the wall's velocity is zero and the ball has a "new" velocity $v' = (v - ov)$. You can then do the calculation as if the wall were stationary, and then move back to the original reference frame (add the velocity of the wall back).



          Note that whey I say add/subtract the velocity of the wall that I mean the velocity as a vector. If your wall is only moving in the $x$ direction, then you only need to adjust the $x$-coordinate.






          share|cite|improve this answer





















          • Thanks it was quite easy to implement in my case and worked really well
            – Matt
            Jan 4 at 15:41
















          0














          This might be better suited for the physics page. That said you should move to a reference frame where the wall is not moving, do the calculation there, and move back.



          To move to the reference frame where the wall is not moving, we need to subtract away the velocity of the wall for everything. Now the wall's velocity is zero and the ball has a "new" velocity $v' = (v - ov)$. You can then do the calculation as if the wall were stationary, and then move back to the original reference frame (add the velocity of the wall back).



          Note that whey I say add/subtract the velocity of the wall that I mean the velocity as a vector. If your wall is only moving in the $x$ direction, then you only need to adjust the $x$-coordinate.






          share|cite|improve this answer





















          • Thanks it was quite easy to implement in my case and worked really well
            – Matt
            Jan 4 at 15:41














          0












          0








          0






          This might be better suited for the physics page. That said you should move to a reference frame where the wall is not moving, do the calculation there, and move back.



          To move to the reference frame where the wall is not moving, we need to subtract away the velocity of the wall for everything. Now the wall's velocity is zero and the ball has a "new" velocity $v' = (v - ov)$. You can then do the calculation as if the wall were stationary, and then move back to the original reference frame (add the velocity of the wall back).



          Note that whey I say add/subtract the velocity of the wall that I mean the velocity as a vector. If your wall is only moving in the $x$ direction, then you only need to adjust the $x$-coordinate.






          share|cite|improve this answer












          This might be better suited for the physics page. That said you should move to a reference frame where the wall is not moving, do the calculation there, and move back.



          To move to the reference frame where the wall is not moving, we need to subtract away the velocity of the wall for everything. Now the wall's velocity is zero and the ball has a "new" velocity $v' = (v - ov)$. You can then do the calculation as if the wall were stationary, and then move back to the original reference frame (add the velocity of the wall back).



          Note that whey I say add/subtract the velocity of the wall that I mean the velocity as a vector. If your wall is only moving in the $x$ direction, then you only need to adjust the $x$-coordinate.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 4 at 14:37









          tchtch

          639210




          639210












          • Thanks it was quite easy to implement in my case and worked really well
            – Matt
            Jan 4 at 15:41


















          • Thanks it was quite easy to implement in my case and worked really well
            – Matt
            Jan 4 at 15:41
















          Thanks it was quite easy to implement in my case and worked really well
          – Matt
          Jan 4 at 15:41




          Thanks it was quite easy to implement in my case and worked really well
          – Matt
          Jan 4 at 15:41











          0














          If the object moves with velocity $vec v_0$ the ball with velocity $vec v$ and the normal at the impact point is $vec n$ then we have:



          $$
          vec v = vec v_{vec n}+vec v_{Pi}\
          vec v_{Pi} = vec v - vec v_{vec n_1} \
          vec v_r = (vec v-vec v_0)_{Pi}-(vec v-vec v_0)_{vec n}\
          vec v_r = (vec v-vec v_0) -2((vec v-vec v_0).vec v_{vec n})vec v_{vec n}
          $$



          with



          $$
          vec v_{vec n} = left(vec vcdotleft(frac{vec n}{||vec n||}right)right)frac{vec n}{||vec n||}
          $$



          where $vec v_r$ represents the reflected ball velocity after collision



          NOTE



          Here $Pi$ represents the plane passing by the impact point with normal $vec n$



          Attached three cases. Here



          $$
          begin{cases}
          vec v mbox{red}\
          vec v_0 mbox{green}\
          vec n mbox{black}\
          Pi mbox{dashed cyan}\
          vec v_r mbox{blue}
          end{cases}
          $$



          enter image description hereenter image description hereenter image description here






          share|cite|improve this answer























          • What are (v⃗ 0)n⃗ and (v⃗ 0)Π ? This is probably a notation i'm not aware of
            – Matt
            Jan 4 at 15:06










          • @Matt Are the components of $vec v_0$ regarding $vec n$ and $Pi$ They are calculated in the same way as $vec v_{vec n}$ and $vec v_{Pi}$
            – Cesareo
            Jan 4 at 15:10










          • Thank you for the time you took to answer, however your answer didn't really help me, the answer below worked fine.
            – Matt
            Jan 4 at 15:42










          • @Matt Some results attached.
            – Cesareo
            Jan 4 at 19:17
















          0














          If the object moves with velocity $vec v_0$ the ball with velocity $vec v$ and the normal at the impact point is $vec n$ then we have:



          $$
          vec v = vec v_{vec n}+vec v_{Pi}\
          vec v_{Pi} = vec v - vec v_{vec n_1} \
          vec v_r = (vec v-vec v_0)_{Pi}-(vec v-vec v_0)_{vec n}\
          vec v_r = (vec v-vec v_0) -2((vec v-vec v_0).vec v_{vec n})vec v_{vec n}
          $$



          with



          $$
          vec v_{vec n} = left(vec vcdotleft(frac{vec n}{||vec n||}right)right)frac{vec n}{||vec n||}
          $$



          where $vec v_r$ represents the reflected ball velocity after collision



          NOTE



          Here $Pi$ represents the plane passing by the impact point with normal $vec n$



          Attached three cases. Here



          $$
          begin{cases}
          vec v mbox{red}\
          vec v_0 mbox{green}\
          vec n mbox{black}\
          Pi mbox{dashed cyan}\
          vec v_r mbox{blue}
          end{cases}
          $$



          enter image description hereenter image description hereenter image description here






          share|cite|improve this answer























          • What are (v⃗ 0)n⃗ and (v⃗ 0)Π ? This is probably a notation i'm not aware of
            – Matt
            Jan 4 at 15:06










          • @Matt Are the components of $vec v_0$ regarding $vec n$ and $Pi$ They are calculated in the same way as $vec v_{vec n}$ and $vec v_{Pi}$
            – Cesareo
            Jan 4 at 15:10










          • Thank you for the time you took to answer, however your answer didn't really help me, the answer below worked fine.
            – Matt
            Jan 4 at 15:42










          • @Matt Some results attached.
            – Cesareo
            Jan 4 at 19:17














          0












          0








          0






          If the object moves with velocity $vec v_0$ the ball with velocity $vec v$ and the normal at the impact point is $vec n$ then we have:



          $$
          vec v = vec v_{vec n}+vec v_{Pi}\
          vec v_{Pi} = vec v - vec v_{vec n_1} \
          vec v_r = (vec v-vec v_0)_{Pi}-(vec v-vec v_0)_{vec n}\
          vec v_r = (vec v-vec v_0) -2((vec v-vec v_0).vec v_{vec n})vec v_{vec n}
          $$



          with



          $$
          vec v_{vec n} = left(vec vcdotleft(frac{vec n}{||vec n||}right)right)frac{vec n}{||vec n||}
          $$



          where $vec v_r$ represents the reflected ball velocity after collision



          NOTE



          Here $Pi$ represents the plane passing by the impact point with normal $vec n$



          Attached three cases. Here



          $$
          begin{cases}
          vec v mbox{red}\
          vec v_0 mbox{green}\
          vec n mbox{black}\
          Pi mbox{dashed cyan}\
          vec v_r mbox{blue}
          end{cases}
          $$



          enter image description hereenter image description hereenter image description here






          share|cite|improve this answer














          If the object moves with velocity $vec v_0$ the ball with velocity $vec v$ and the normal at the impact point is $vec n$ then we have:



          $$
          vec v = vec v_{vec n}+vec v_{Pi}\
          vec v_{Pi} = vec v - vec v_{vec n_1} \
          vec v_r = (vec v-vec v_0)_{Pi}-(vec v-vec v_0)_{vec n}\
          vec v_r = (vec v-vec v_0) -2((vec v-vec v_0).vec v_{vec n})vec v_{vec n}
          $$



          with



          $$
          vec v_{vec n} = left(vec vcdotleft(frac{vec n}{||vec n||}right)right)frac{vec n}{||vec n||}
          $$



          where $vec v_r$ represents the reflected ball velocity after collision



          NOTE



          Here $Pi$ represents the plane passing by the impact point with normal $vec n$



          Attached three cases. Here



          $$
          begin{cases}
          vec v mbox{red}\
          vec v_0 mbox{green}\
          vec n mbox{black}\
          Pi mbox{dashed cyan}\
          vec v_r mbox{blue}
          end{cases}
          $$



          enter image description hereenter image description hereenter image description here







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Jan 4 at 19:13

























          answered Jan 4 at 14:26









          CesareoCesareo

          8,3413516




          8,3413516












          • What are (v⃗ 0)n⃗ and (v⃗ 0)Π ? This is probably a notation i'm not aware of
            – Matt
            Jan 4 at 15:06










          • @Matt Are the components of $vec v_0$ regarding $vec n$ and $Pi$ They are calculated in the same way as $vec v_{vec n}$ and $vec v_{Pi}$
            – Cesareo
            Jan 4 at 15:10










          • Thank you for the time you took to answer, however your answer didn't really help me, the answer below worked fine.
            – Matt
            Jan 4 at 15:42










          • @Matt Some results attached.
            – Cesareo
            Jan 4 at 19:17


















          • What are (v⃗ 0)n⃗ and (v⃗ 0)Π ? This is probably a notation i'm not aware of
            – Matt
            Jan 4 at 15:06










          • @Matt Are the components of $vec v_0$ regarding $vec n$ and $Pi$ They are calculated in the same way as $vec v_{vec n}$ and $vec v_{Pi}$
            – Cesareo
            Jan 4 at 15:10










          • Thank you for the time you took to answer, however your answer didn't really help me, the answer below worked fine.
            – Matt
            Jan 4 at 15:42










          • @Matt Some results attached.
            – Cesareo
            Jan 4 at 19:17
















          What are (v⃗ 0)n⃗ and (v⃗ 0)Π ? This is probably a notation i'm not aware of
          – Matt
          Jan 4 at 15:06




          What are (v⃗ 0)n⃗ and (v⃗ 0)Π ? This is probably a notation i'm not aware of
          – Matt
          Jan 4 at 15:06












          @Matt Are the components of $vec v_0$ regarding $vec n$ and $Pi$ They are calculated in the same way as $vec v_{vec n}$ and $vec v_{Pi}$
          – Cesareo
          Jan 4 at 15:10




          @Matt Are the components of $vec v_0$ regarding $vec n$ and $Pi$ They are calculated in the same way as $vec v_{vec n}$ and $vec v_{Pi}$
          – Cesareo
          Jan 4 at 15:10












          Thank you for the time you took to answer, however your answer didn't really help me, the answer below worked fine.
          – Matt
          Jan 4 at 15:42




          Thank you for the time you took to answer, however your answer didn't really help me, the answer below worked fine.
          – Matt
          Jan 4 at 15:42












          @Matt Some results attached.
          – Cesareo
          Jan 4 at 19:17




          @Matt Some results attached.
          – Cesareo
          Jan 4 at 19:17


















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