Bernard Shepherd was charged with two counts of aggravated battery and two counts of aggravated assault based on the shooting of victim Kevin Roseberry. He pled not guilty to the charges and elected to be tried before a judge sitting without a jury.
At the bench trial, Roseberry testified that he saw Shepherd, whom he has known for many years, and another man, Eric Pressly, getting into a van. Roseberry walked up to the van and asked Shepherd for cocaine. Shepherd gave Roseberry some cocaine, and Rose-berry then asked if he could pay for it the next day. Shepherd said he could not pay for it the next day and told Roseberry to return the cocaine. When Roseberry did not return the cocaine and continued to ask if he could pay for it the next day, Shepherd got out of the van with a handgun. As Shepherd confronted Roseberry, Pressly shot Roseberry in the face with a shotgun. Shepherd then shot Roseberry in the chest and leg with the handgun. After the shootings, Shepherd and Pressly fled from the scene in the van. An ambulance arrived a short time later and took Roseberry to the hospital, where he told a police detective that Shepherd and Pressly had shot him. As a result of the shootings, Roseberry lost his left eye and has only ten percent vision in his right eye.
A police detective confirmed that he spoke with Roseberry at the hospital. The detective testified that Roseberry identified Shepherd and Pressly as the persons who had shot him, described the two men, and told him where they lived. Based on Roseberry’s information, the police secured arrest warrants for Shepherd and Pressly, although at the time of trial Pressly had not yet been apprehended.
Shepherd and the state stipulated that the results of Shepherd’s polygraph examination were admissible at the trial. The polygraph examiner testified that Shepherd was deceptive when questioned about the shooting of Roseberry and that, according to the polygraph *387results, Shepherd was involved in the shooting. The examiner stated that the results of such a properly administered test are 97 to 98 percent accurate.
In his defense, Shepherd presented the alibi that he was at his sister’s house at the time of the shooting. He and his sister testified that he had gotten off work several hours before the shooting and gone directly to his sister’s house. They claimed that he spent the night there and did not leave the house until the next morning, after the shooting had occurred.
After considering the evidence, the court found Shepherd guilty of two counts of aggravated battery and one count of aggravated assault and not guilty of the other aggravated assault count. The court merged the two aggravated battery counts and sentenced Shepherd to serve fifteen years in prison followed by five years on probation.
Shepherd appeals, arguing that there is insufficient evidence to support his convictions, that the court erred in not sequestering Roseberry before hearing his testimony, and that the court erred in not allowing Shepherd to cross-examine Roseberry about whether he paid court-ordered child support. Shepherd’s arguments are without merit, and we therefore affirm his convictions.
1. On appeal from a criminal conviction, we no longer presume that the appellant is innocent, and we view the evidence in the light most favorable to the verdict to determine if a rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.1
In the instant case, a rational trier of fact could have found the essential elements of aggravated battery2 and aggravated assault3 beyond a reasonable doubt based on Roseberry’s in-court identification of Shepherd as one of the men who shot him, the detective’s confirmation that shortly after the shootings Roseberry identified Shepherd as one of his assailants, and the polygraph examiner’s testimony that the polygraph results show that Shepherd was involved in the shooting of Roseberry.
As for the believability of Shepherd’s alibi evidence and the credibility of the witnesses, those were matters to be resolved by the trial judge sitting as the factfinder.4 The trial judge was certainly authorized to disbelieve Shepherd’s claim of an alibi.5 Because there was *388sufficient evidence to support the trial court’s findings of guilt beyond a reasonable doubt, Shepherd’s convictions must be affirmed.
Decided July 27, 2000.
2. OCGA § 24-9-61, the rule of sequestration, provides that a party has the right to have the witnesses of the other party examined out of the hearing of each other, except as otherwise provided in OCGA § 24-9-61.1. Under OCGA § 24-9-61.1 (a), a trial judge has the discretion to allow a crime victim to be present in court and the discretion to determine the order in which the victim’s testimony will be given.6
In this case, the trial judge allowed the victim Roseberry to remain in the courtroom while the detective and the polygraph examiner testified and then let him give his own testimony. Under OCGA §§ 24-9-61 and 24-9-61.1 (a), such a procedure was fully within the trial court’s discretion and does not constitute reversible error.7
3. A trial court does not abuse its discretion in limiting a defendant’s cross-examination only to relevant matters.
(Although a defendant has a right to a thorough and sifting cross-examination of the witness, the scope of cross-examination is not unlimited, and the extent of examination is largely within the discretion of the trial judge and will not be controlled by an appellate court except for abuse of discretion. Moreover, although the Georgia rule favors the admission of any relevant evidence, no matter how slight its probative value, the admission or exclusion of evidence which is objected to on the ground of relevancy lies within the sound discretion of the trial court.8
In the present case, the trial court sustained the state’s relevancy objection to Shepherd’s attempt to cross-examine Roseberry about whether he was paying court-ordered child support. We agree with the trial court that the question of Roseberry’s child support was irrelevant to the ultimate issue in the case — whether Shepherd committed the charged offenses. The trial court did not abuse its discretion in prohibiting the cross-examination on an irrelevant matter.9
Judgment affirmed.
Smith, P. J, and Phipps, J., concur.
*389Richard W. Marks, for appellant.
J Tom Morgan, District Attorney, Barbara B. Conroy, Maria Murder-Ashley, Assistant District Attorneys, for appellee.