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Asked: 2026-06-07T19:13:26+00:00

I have a sprite that moves along a vector (-0.7,-0.3). I have another point

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I have a sprite that moves along a vector (-0.7,-0.3). I have another point whose coordinates I have – let’s call them (xB|yB). Now, quite some time ago I learned to calculate the perpendicular distance from a vector to a point (first formula on this page http://en.wikipedia.org/wiki/Perpendicular_distance). However I tried it, and if I log it, it returns an unbelievably high value that is 100% false. So what do I do wrong ? Have a look at the image I provided.

incomingVector = (-0.7,-0.3) //this is the vector the sprite is moving along

bh.position is the point I want to calculate the distance to

Here is the code: 

        // first I am working out the c Value in the formula in the link given above
        CGPoint pointFromVector = CGPointMake(bh.incomingVector.x*theSprite.position.x,bh.incomingVector.y*theSprite.position.y);
        float result = pointFromVector.x + pointFromVector.y;
        float result2 = (-1)*result;

        //now I use the formula
        float test = (bh.incomingVector.x * bh.position.x + bh.incomingVector.y * bh.position.y + result2)/sqrt(pow(bh.incomingVector.x, 2)+pow(bh.incomingVector.y, 2));

        //the distance has to be positive, so I do the following
        if(test < 0){
            test *= (-1);
        }
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1 Answer

  1. Editorial Team

    let us implement the formula again, according to the contents of your original link.

    • we have a vector for the line: V(a; b)
    • we have a point on the line (the centre of the sprite): P(x1, y1)
    • we have another point somewhere else: B(xB, yB)

    for the testing here are two rows of random values:

    1. a = -0.7; b = -0.3; x1 = 7; y1 = 7; xB = 5; yB = 5;
    2. a = -0.7; b = -0.3; x1 = 7; y1 = 7; xB = 5.5; yB = 4;

    the numerator is the following then: (it seems you are calculating the numerator an unknown way, I don’t understand why you did it because this is the proper way to calculate the numerator for the linked formula, perhaps this is why you got totally wrong distances.)

    float _numerator = abs((b * xB) - (a * yB) - (b * x1) + (a * y1));
// for the 1. test values: (-0.3 * 5) - (-0.7 * 5) - (-0.3 * 7) + (-0.7 * 7) = -1.5 + 3.5 + 2.1 - 4.9 = -0.8 => abs(-0.8) = 0.8
// for the 2. test values: (-0.3 * 5.5) - (-0.7 * 4) - (-0.3 * 7) + (-0.7 * 7) = -1.65 + 2.8 + 2.1 - 4.9 = -1.65 => abs(-1.65) = 1.65

    the denominator is the following then:

    float _denomimator = sqrt((a * a) + (b * b));
// for the 1. test values: (-0.7 * -0.7) + (-0.3 * -0.3) = 0.49 + 0.09 = 0.58 => sort(0.58) = 0.76
// for the 2. test values: (-0.7 * -0.7) + (-0.3 * -0.3) = 0.49 + 0.09 = 0.58 => sort(0.58) = 0.76

    the distance is obvious now:

    float _distance = _numerator / _denominator;
// for the 1. test values: 0.8 / 0.76 = 1.05
// for the 2. test values: 1.65 / 0.76 = 2.17

    and these results (1.05 and 2.17) are the correct distances exactly for our random values, if you can draw the lines and the points on the paper you can measure the distance and you would get the same values, using standard ruler.

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