Tile slopes and jittery movement

Question

I'm trying to handle slopes in a tiles based world. I'm using basic linear interpolation to find the Y coordinate of the character based on his X position. But i have a problem, when the character move up or down the slopes the sprite is all jittery, it doesn't move smoothly and i can't figure out why.

I don't use a "true physics engine" all the engine does is AABB collision and tell when a collision occurs and let you handle the reaction. When the character is on a slope no "gravity" (Y velocity) is applied the Y position is adjusted by hand using the linear interpolation result.

Here is the linear interpolation function that i use :

float InterpolateY(Vector2 point1, Vector2 point2, float x)
{
    float x1 = point1.X;
    float y1 = point1.Y;

    float x2 = point2.X;
    float y2 = point2.Y;

    float y = y1 + (x - x1) * (y2 - y1) / (x2 - x1);

    return y;
}

I've made a webm to show you the problem (ignore the fact that the sprite sink into other tile it doesn't matter for the moment)

Link to the webm : https://webmshare.com/play/vPXLD

Answer 1

I suspect that the engine is doing that. Basically the character is colliding but is getting pushed away from the collider of the ground.
When I used Unity similiar problems occured.
I think its a Physics/Engine Problem

Answer 2

I found the problem, it was pretty obvious actually. The position of the character was calculated using a motion vector and the motion.X used in the interpolation was a float number so the result was also a float number (ex : 125.5). The problem happen when i put my character to the Y position calculated (a float) on the screen, the screen coordinate are integers so the Y value get rounded (ex : 125.5 -> 125) thats why i got this jittery effect.