# Angle between two points in Cartesian coordinate system C++

I'm trying to rotate a rectangle so that it faces another rectangle in a spiral.

Im using the Bullet pyhics library and freeglut for the 3d application, for anyone interested https://github.com/damorton/bullet-dominos float x = 0;
float z = 0;
float angle = 0.0f;
int a = 2, b = 2;
float previousX = 0.0f;
float previousZ = 0.0f;

for (int i = 4; i < maxPoints; i++)
{
angle = 0.1 * i;
x = (a + b * angle) * cos(angle);
z = (a + b * angle) * sin(angle);

GameObject* temp = CreateGameObject(x, 0, z);

float newAngle = atan2(previousZ - z, previousX - x) * 180 / PI;
temp->setRotationYaw(newAngle);

previousX = x;
previousZ = z;
}


You can see from the top view that the rectangles are not pointing towards the previous rectangles position. EDIT: After trying the below code

float x = 0;
float z = 0;
float angle = 0.0f;
int a = 2, b = 2;
float previousX = 0.0f;
float previousZ = 0.0f;

for (int i = 0; i < maxPoints; i++)
{
angle = 0.1 * i;
x = (a + b * angle) * cos(angle);
z = (a + b * angle) * sin(angle);

GameObject* temp = CreateGameObject(x, 0, z);

float dirX = -(a + b * angle) * sin(angle) + b * cos(angle);
float dirZ = (a + b * angle) * cos(angle) + b * sin(angle);
float newAngle = atan2(dirZ, dirX) * 180 / PI;
temp->setRotationYaw(newAngle);

previousX = x;
previousZ = z;
}


The result is: Console output: EDIT: Solution. Some things to note are that the result of atan2() was not converted to degrees using atan2() * 180 / PI. Also that I passed in atan2(X, Z) compared to atan2(Z, X) that is sometimes done for hysterical raisins http://www2.tcl.tk/10814.

// create spiral dominos
float x = 0;
float z = 0;
float angle = 0.0f;
int a = 2, b = 2;
float previousX = 0.0f;
float previousZ = 0.0f;

float dominoHeight = 2.0f;

for (int i = 2; i < maxPoints; i++)
{
if (i % 30 == 0) dominoHeight++;

angle = 0.15 * i;
x = (a + b * angle) * cos(angle);
z = (a + b * angle) * sin(angle);

GameObject* temp = CreateGameObject(x, 0, z);

float dirX = -(a + b * angle) * sin(angle) + (b * cos(angle));
float dirZ = (a + b * angle) * cos(angle) + (b * sin(angle));
float newAngle = atan2(dirX, dirZ);
printf("dirX: %f - dirZ: %f - angle: %f\n", dirX, dirZ, newAngle);
temp->setRotationYaw(newAngle);

previousX = x;
previousZ = z;
} • It would be nice if you could include in your post what libraries you use. Your using Unity right? – joojaa Dec 27 '15 at 15:35
• Using Bullet physics and freeglut – David Dec 27 '15 at 15:39
• Not Unity github.com/damorton/bullet-dominos – David Dec 27 '15 at 22:06

The parametric equation for a spiral is:

\begin{eqnarray} \begin{aligned} x &= &(a + b \theta) \times \cos(\theta)\\ z &= &(a + b \theta) \times \sin(\theta) \end{aligned} \end{eqnarray}

The direction on the spiral point is simply the derivative of the system with respect to $\theta$. Thus the direction is:

\begin{eqnarray} \begin{aligned} x_{dir} &=&-(a + b \theta) \times \sin(\theta) + b \times \cos(\theta)\\ z_{dir} &=&(a + b \theta) \times \cos(\theta) + b \times \sin(\theta) \end{aligned} \end{eqnarray}

Finally angle is is simply atan2 of the direction equation. Image 1: This is what I get when i plot squares at $(x, z)$ with direction $(x_{dir}, z_{dir})$

Mathematica source for image

• I tried float dirX = -(a + b * angle) * sin(angle) + b * cos(angle); and float dirZ = (a + b * angle) * cos(angle) + b * sin(angle);  then float newAngle = atan2(dirZ, dirX); but this does not set the angle correctly. – David Dec 27 '15 at 14:38
• I'm multiplying the result by 180 * Pi to convert to radians – David Dec 27 '15 at 14:52
• Programming language is c++ – David Dec 27 '15 at 14:57
• Atan2 c++ cplusplus.com/reference/cmath/atan2 – David Dec 27 '15 at 15:02
• ill update the question with what I have so far can you have a look? – David Dec 27 '15 at 15:13