How can we convert coordinates of a 3D object into a 2D image?

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You use a projection matrix — 3D projection

For example:

1. mat4x4 makeProj(float fFovDegrees, float fAspectRatio,
2. float fNear, float fFar)
3. {
4. float fFovRad = 1.0f / tanf(fFovDegrees * 0.5f /
5. 180.0f * 3.14159f);
6. mat4x4 matrix;
7. matrix.m[0][0] = fAspectRatio * fFovRad;
8. matrix.m[1][1] = fFovRad;
9. matrix.m[2][2] = fFar / (fFar — fNear);
10. matrix.m[3][2] = (-fFar * fNear) / (fFar — fNear);
11. matrix.m[2][3] = 1.0f;
12. matrix.m[3][3] = 0.0f;
13. return matrix;
14. }
15. mat4x4 matProj = makeProj(90,
16. (float)SCREEN_HEIGHT / (float)SCREEN_WIDTH,
17. 0.1f, 1000.0f);
18. for (triangle& tri : gameObj.tris) {
19. triangle triProj;
20. triProj.p[0] = matProj * tri.p[0];
21. triProj.p[1] = matProj * tri.p[1];
22. triProj.p[2] = matProj * tri.p[2];
23. // do stuff with triProj, which is now 2D
24. }