[Gambas-user] more trigonometry fun (not)

[Kevin Fishburne]

On 05/24/2011 12:57 AM, Bruce Bruen wrote:
> On 24/05/11 14:08, Kevin Fishburne wrote:
>> On 05/24/2011 12:16 AM, Bruce Bruen wrote:
>>
>>> On 24/05/11 13:14, Kevin Fishburne wrote:
>>>
>>>> I was already helped graciously in figuring out how to translate a point
>>>> in a plane along its local axes at a given orientation, but now need a
>>>> bit of the inverse of the equation.
>>>>
>>>> I need to know the (x, y) offset of a point at a given orientation and
>>>> velocity. For example if a point is moving at an angle of 45 degrees (or
>>>> radians, take your pick), what would its x and y coordinate be
>>>> increased/decreased by? The variables I can think of would be:
>>>>
>>>> x1 (point's current x coordinate)
>>>> y1 (point's current y coordinate)
>>>> a (point's angle/orientation in degrees/radians)
>>>> v (point's velocity)
>>>> x2 (x coordinate offset of point's new position)
>>>> y2 (y coordinate offset of point's new position)
>>>>
>>>> The calculation would take x1, y1 a and v as inputs and produce x2 and
>>>> y2 as offsets (x1 + x2, y1 + y2 = point's new position).
>>>>
>>>> There really should be a list of basic things like this for graphics
>>>> programmers. I've searched for years and found practically nothing.
>>>> Weird, considering this has probably been done thousands of times since
>>>> the days of DOS. :/
>>>>
>>>> In case anyone's wondering why I need this, the equation will allow
>>>> particles and projectiles to follow logical paths. Currently they're
>>>> bound to local coordinates and ignore player orientation. Digging,
>>>> shooting arrows, throwing objects, etc. can't work without it.
>>>>
>>>>
>>>>
>>> 1) Need to include i being the time increment in the same units as velocity
>>> 2) Basic physics says point will move d units in i time increments according
>>> to distance=velocity * time . So point will have a deltaXY of v*i.
>>> Basic trig converts this to deltaX and deltaY using the old "Sign On
>>> Here 'Coz Alf Has Tan OverAlls"
>>> deltaX = deltaXY * sin(a)
>>> deltaY=deltaXY *cos(a)
>>>
>>> Bobs, yer uncle, return deltaX and deltaY!
>>>
>> Very true. I didn't want to include time because I didn't want to
>> complicate the issue. Time is basically whatever number I multiply the
>> velocity by in the mystical and unknown equation. In my case time is a
>> single rendering frame, so it's not currently tied to any real sense of
>> the word "time".
>>
>> While I appreciate the hint, what's the equation for DeltaX/Y using
>> Sin/Cos/Tan if that is what's being used? I think you may be a bit more
>> under the weather than I. :) And it's not even Friday... Fortunately
>> when I cross the threshold I stop programming and write music for the
>> game. A much more forgiving medium for sure.
>>
>>
> Not sure I understand "what's the equation for DeltaX/Y"?
> Did you mean deltaXY?  If so it's just v*i as stated.

I think you're helping too much! I just need a basic formula for moving 
a point along a certain angle by a certain number of units. The angle of 
movement, the velocity (number of units divided by time) and the 
original coordinates are all known. The only unknown is how much the 
point's x and y coordinates should be modified by using 
addition/subtraction.

Imagine you're looking at a piece of graph paper. You have a point drawn 
as a dot in pencil on an intersection of the grid. You need to move that 
point one unit/square in a any direction as specified in radians or 
degrees. It's 2D, there's no gravity, wind or curvatures of any kind. No 
allowance is necessary for other variables or factors. That is the 
equation that I need. Move the point an arbitrary number of units in an 
arbitrary direction. Point position, units moved and angle of movement 
known; new point position is unknown.

-- 
Kevin Fishburne
Eight Virtues
www: http://sales.eightvirtues.com
e-mail: sales at ...1887...
phone: (770) 853-6271