¶ 1 In our increasingly computerized world, attorneys often present video depictions of events at trial to explain how those events occurred. This appeal involves the question whether three video depictions were admissible in a criminal trial. To answer this question, we must decide whether the videos were "animations" or "simulations," which are two terms of art.
¶ 2 As a general matter, an animation is based on information that an expert has gathered and the opinions that the expert has reached based on that information. The animation then depicts the expert's opinion of how the event occurred.
¶ 3 A simulation is different. A computer program does the work of reaching the opinion based on the information, or it at least assists the expert in figuring out what his or her opinion should be. The simulation then depicts how the event actually occurred based wholly, or at least in part, on the computer's analysis.
¶ 4 At the end of the trial in this case, a jury convicted defendant, Joseph Douglas, of leaving the scene of an accident, failure to report an accident, and careless driving. He appeals the judgment of conviction and the trial court's order that required him to pay an insurer $37,717.28 in restitution.
¶ 5 Defendant contends that the trial court should not have allowed the prosecution to show the jury three short video depictions of an automobile-bicycle collision. He asserts that they were simulations, and that the prosecution did not lay an adequate foundation to support the court's decision to admit them. We disagree because we conclude that the videos were animations and that the prosecution laid a sufficient foundation.
*1030¶ 6 We therefore affirm the judgment of conviction. We also affirm the trial court's restitution order.
I. Background and Procedural History
¶ 7 In August 2011, defendant was driving his car on a two-lane, rural road around dusk on a windy day. He took his eyes off the road for a few seconds to look at his radio. The passenger side of his car struck a bicyclist who was riding in the same direction on the side of the road. She flew through the air for a distance, and she landed in a ditch, which was filled with chest-high vegetation.
¶ 8 The collision and the resulting fall broke the bicyclist's leg and sprained her wrist. She managed to climb out of the ditch, and she then called for emergency assistance on her cell phone.
¶ 9 Defendant drove away. He later claimed that he had not seen the bicyclist. He had felt the side of his car strike her, but, when he stopped to look around, he did not see her or her bicycle. So he assumed that his car had struck a deer.
¶ 10 As is relevant to this appeal, the prosecution charged defendant with leaving the scene of an accident, failure to report an accident, and careless driving resulting in injury.
¶ 11 The prosecution informed defendant that it intended to introduce three video depictions of the collision at trial. A state trooper who was an accident reconstruction expert had prepared them. The depictions showed the collision from different angles.
¶ 12 Defendant filed a motion to exclude the three videos. Relying on CRE 702 and People v. Shreck, 22 P.3d 68 (Colo.2001), the motion asserted that the videos were simulations and that they were not admissible because they were based on (1) "unreliable analysis, unreliable data," and an "unreliable program"; and (2) "only partial[ly] self-reported data." Alternatively, defendant contended that even if the videos were animations, they were nonetheless inadmissible because they did not fairly and accurately depict the collision.
¶ 13 The trial court held an evidentiary hearing. The prosecutor asserted that the videos were animations. Defense counsel responded that her "main concern" was that the facts depicted in the videos were in dispute. She said that the "problem is whether [the videos were] ... fair and accurate representation of what happened." (As we will explain below, part of the foundation for admitting animations is that they fairly and accurately depict an event.) She reiterated that she also thought that the videos were simulations.
¶ 14 The prosecutor conceded that the videos "entail[ed] a fair amount of math and science." But, the prosecutor's argument continued, they were animations because they were based on the measurements that the trooper had taken at the scene of the collision, information that some witnesses had provided to him, and calculations that he had performed before he used a computer to create the videos.
¶ 15 The trial court decided that the videos were animations and that it would allow the jury to watch them at trial. The court also found that (1) they were relevant because they would provide the jury with visual depictions of the collision and because they showed the relative positions of the car and the bicycle on the road; (2) they were fair and accurate depictions of the collision; (3) any discrepancies between the videos and other evidence went to their weight, not to their admissibility; and (4) the probative value of the videos was not substantially outweighed by any prejudice that defendant might suffer if the jury watched them.
¶ 16 When the prosecutor showed the videos at trial, the court gave the jury a limiting instruction. The instruction stated that the videos represented the trooper's opinion about how the collision had occurred. The court also limited the jury to watching the videos twice: once during the trooper's testimony and once during the jury's deliberations.
II. The Videos Were Animations
¶ 17 Defendant asserts that the videos were simulations and that they were scientific evidence. The prosecution therefore had to show that they were admissible under the test found in CRE 702 and Shreck, 22 P.3d at 82-83.
*1031¶ 18 Alternatively, defendant contends that even if the videos were animations, the court should not have admitted them because they did not meet the necessary foundational requirements.
¶ 19 We disagree with both of these contentions.
A. Standard of Review
¶ 20 We review a trial court's evidentiary rulings for abuse of discretion. People v. Ibarra, 849 P.2d 33, 38 (Colo.1993). We will not reverse an evidentiary ruling unless the decision was manifestly arbitrary, unreasonable, or unfair, or if it was based on an erroneous understanding or application of the law. Salazar v. Kubic, 2015 COA 148, ¶ 6, --- P.3d ----.
B. Animations v. Simulations
1. Legal Principles
¶ 21 As is pertinent to this appeal, computer-generated video depictions of events fall into two categories: animations and simulations. People v. Cauley, 32 P.3d 602, 606-07 (Colo.App.2001) ; see Lorraine v. Markel Am. Ins. Co., 241 F.R.D. 534, 559 (D.Md.2007). There are different foundational elements for the admission of videos based on the category in which they belong.
¶ 22 On the one hand, courts view animations as demonstrative evidence. Cauley, 32 P.3d at 607. The proponent of an animation must (1) authenticate it; (2) show that it is relevant; (3) show that it is a "fair and accurate representation of the evidence to which it relates"; and (4) show that its probative value is not substantially outweighed by the danger of unfair prejudice. Id.
¶ 23 On the other hand, courts consider simulations to be scientific evidence. Id. ; see Lorraine, 241 F.R.D. at 560. Simulations are offered as substantive, not demonstrative, evidence. Bullock v. Daimler Trucks N. Am., LLC, 819 F.Supp.2d 1172, 1176 (D.Colo.2011) ; Lorraine, 241 F.R.D. at 560 ; Tull v. Fed. Express Corp., 197 P.3d 495, 499 (Okla.Civ.App.2008). A simulation depends on the proper application of scientific principles, so its admissibility hinges on whether it meets the foundational requirements of scientific evidence. Cauley, 32 P.3d at 606-07.
¶ 24 There are some similarities between animations and simulations. They can both require someone to input data into a computer program. See Bullock, 819 F.Supp.2d at 1175-1177 (data input not determinative of categorization as simulation or animation); State v. Tollardo, 134 N.M. 430, 77 P.3d 1023, 1028 (Ct.App.2003) (same). They can both depict recreations of events. Cauley, 32 P.3d at 607 ; see generally Clark v. Cantrell, 339 S.C. 369, 529 S.E.2d 528 (2000). They can both use scientific principles to recreate those events. See, e.g., Pino v. Gauthier, 633 So.2d 638, 652 (La. Ct. App.1993) (considering simulation created by inputting vehicle weight, speed, road conditions, and braking data into a specialized computer); Clark, 529 S.E.2d at 537 (stating that accident recreation animation must correctly show distance, terrain, relative speed, path of travel, and surroundings).
¶ 25 But, based on the preceding discussion, there are clear differences that distinguish animations and simulations. We introduce our discussion of those differences, which we explain in more detail below, by providing the reader with the following chart.
2. Differences
¶ 26 There are two questions that highlight the primary differences between animations and simulations.
(1) Who, or what, is the source of the opinion?
(2) How does the proponent of the depiction intend to use it at trial?
a. Source of the Opinion
¶ 27 On the one hand, an animation "simply illustrates an opinion or reconstruction which an expert witness has already devised through the expert's own independent computation and analyses." Commonwealth v. Serge, 58 Pa. D. & C.4th 52, 70 (Ct. Com. Pl. Lackawanna Cty., Pa.2001). An animation does not generate the expert's opinion, and it does not provide missing information. See Tollardo, 77 P.3d at 1029 ; Tull, 197 P.3d at 499. Rather, it visually depicts information that someone has entered into the computer program. Bullock, 819 F.Supp.2d at 1176 ; Clark, 529 S.E.2d at 535. Animations can be viewed as "labor saving device[s]"-they save an expert the trouble of having to draw diagrams by hand. Constans v. Choctaw Transp., Inc., 712 So.2d 885, 901 (La.Ct.App.1997) ; see also Serge, 58 Pa. D. & C.4th at 69.
¶ 28 On the other hand, in a simulation, the computer functions independently-it is like an "expert" itself. It renders its own "opinion" based on its internal calculations. Tull, 197 P.3d at 499 ; see Constans, 712 So.2d at 901. The expert may enter the data or the scientific principles, but the computer program analyzes the data to produce the conclusion. See Cauley, 32 P.3d at 606 ; see also Lorraine, 241 F.R.D. at 559 ; Serge, 58 Pa. D. & C.4th at 69-70. Even if an expert uses a computer's preliminary conclusions to reach his or her ultimate conclusions, the result is still a simulation because the computer was the source of the preliminary conclusions. Tollardo, 77 P.3d at 1028 ; Tull, 197 P.3d at 499.
b. Intended Use at Trial
¶ 29 When a computer-generated depiction does not supply missing information-meaning that an expert has arrived at an opinion without using the computer-the evidence only functions demonstratively. Tull, 197 P.3d at 499. The depiction is demonstrative because it mirrors a witness's testimony. Id. It is simply a more technologically savvy depiction of what the expert could have offered if he or she had used a series of explanatory drawings. Id. ("An animation can be thought of as a series of diagrams that have been strung together to produce a moving image."); see Constans, 712 So.2d at 901 (animation saved the expert from having to draw his own diagrams by hand). A depiction that satisfies these criteria is an animation.
¶ 30 An animation is not subject to the more rigorous scientific evidence standard found in CRE 702 and Shreck. It *1033functions as, and the jury understands it to be, a visual depiction of the expert's theory about how an accident occurred, as opposed to a computer's recreation of the actual event. Hinkle v. City of Clarksburg, 81 F.3d 416, 425 (4th Cir.1996) ; Serge, 58 Pa. D. & C.4th at 70. The opinions depicted in the animation are the expert's, so they can then be explored and cross-examined through testimony. Tollardo, 77 P.3d at 1028. The foundational requirements adopted in Cauley mitigate any unduly persuasive power that a video depiction might have. 32 P.3d at 607. Courts are also encouraged to give a limiting instruction that explains that an animation is "only a re-creation of the proponent's version of the event." Clark, 529 S.E.2d at 537 ; see Bullock, 819 F.Supp.2d at 1176.
¶ 31 If the computer-generated evidence is used to supply missing information to prove a disputed material fact in a case, it functions as substantive scientific evidence. See Pierce v. State, 718 So.2d 806, 808 (Fla.Dist.Ct.App.1997). So the validity of the conclusions that the computer drew depends on the computer's proper application of scientific principles. Cauley, 32 P.3d at 606. A computer that uses such principles to reach a scientific conclusion is a simulation.
¶ 32 Simulations are subject to the admissibility standards for scientific evidence because (1) they function as recreations of the actual event; (2) the "extreme vividness," Clark, 529 S.E.2d at 536 (quoting State v. Trahan, 576 So.2d 1, 8 (La.1990) ), and persuasive power of a video can create an "exaggerated aura of computer infallibility," Constans, 712 So.2d at 901 ; and (3) unlike a witness, an attorney cannot cross-examine a computer about its conclusions. Tollardo, 77 P.3d at 1028 ; Serge, 58 Pa. D. & C.4th at 70.
3. Analysis
¶ 33 Defendant contends that the videos were simulations because the computer applied the laws of physics to depict the collision. He adds that the computer software that created the videos conducted its own internal calculations and drew its own conclusions. But we conclude that the record of how the trooper prepared the videos does not support defendant's contention.
¶ 34 First, the record shows that the trooper, not the computer's software, supplied the calculations and the opinions that the computer used to create the videos. Cauley, 32 P.3d at 606. The videos were therefore merely graphic representations of a series of pictures that the trooper could have drawn himself. See Serge, 58 Pa. D. & C.4th at 69. For example, the trooper reached his own conclusions about (1) the distance between defendant's car and the bicycle when defendant looked down at his radio; (2) how the car struck the bicycle; (3) the trajectories of the victim and of the bicycle after the car struck them; and (4) where the victim and the bicycle landed after the collision.
¶ 35 Second, the trooper formed many of his opinions based on his examination of the physical evidence. For example, he testified that the damage to the mirror on the passenger side of defendant's car was "consistent with the vehicle's forward movement ... traveling fast." He said that the damage to the car's windshield suggested the trajectory of the bicyclist after the collision because the damage was "consistent with soft body tissue." He formed an opinion about the bicycle's trajectory by "looking at the damage on the bicycle itself." And he added that his analysis of the combined damage to the car and to the bicycle led him to form the opinions that the "right front corner [of the car] touch[ed] ... the left outside of the [bicycle's] tire" and that the corner of the car then struck the bicycle's left pedal and the bicyclist's left leg. This contact caused the bicycle "to rotate in a clockwise orientation."
¶ 36 Third, the trooper based his opinion about the approximate geographic location of the collision on his analysis of the posted speed limit, the bicyclist's statement about how fast she was going, and the location of the debris from the collision that another police officer had found during the investigation.
¶ 37 Fourth, the orientation of the bicycle and the car in the videos "was based completely on physical evidence"-the damage to the car and to the bicycle, plus the location of the debris-and the bicyclist's "post-impact trajectory." The trooper stated that his *1034analysis was based on "movement, laws of motion, and physics."
¶ 38 Fifth, the trooper did his own mathematical calculations based on measurements that he had taken. For example, he determined there were about 286 feet between the car and the bicycle when defendant looked down at his radio. The trooper did not suggest that any of his analysis was the result of, or was supplemented by, any mathematical calculations that the computer may have performed. Compare Tull, 197 P.3d at 499 (finding computer-generated animation did not represent any substantive addition to expert's testimony), with Tollardo, 77 P.3d at 1028-29 (determining that the expert used the computer to develop an opinion based in part on computer-generated evidence). And, when the prosecutor asked the trooper how he had come to his conclusion that defendant had not seen the bicyclist before the collision, the trooper responded that he had relied on "the damaged bike, the injured person, the damaged vehicle, and [defendant's] statement that he ha[d] no idea something was there."
¶ 39 Sixth, the videos functioned as a demonstrative exhibit that illustrated the trooper's opinion. He used the videos to recreate his theory of how the collision occurred based on his analysis; he did not use them to recreate the actual accident. See Serge, 58 Pa. D. & C.4th at 69.
¶ 40 Seventh, the jury knew that the videos were illustrations of the trooper's theory of how the collision had occurred and not a recreation of the actual event. See id. at 70. The trooper conceded on cross-examination that he had relied on facts that the bicyclist had provided and that defendant had disputed. The trooper also conceded that the videos could not show what defendant would have seen if he had been "looking straight at the sun." And the trial court's limiting instruction stated that the videos had been admitted to "help the [trooper] explain, in his opinion, the manner in which the accident occurred." (Emphasis added.)
¶ 41 We therefore conclude the trial court did not abuse its discretion when it decided that the videos were animations. We therefore further conclude that the court was not required to analyze them under CRE 702 and Shreck .
¶ 42 We now turn to the question whether the trial court abused its discretion when it admitted the videos into evidence as animations.
C. Admission of Animations
¶ 43 Defendant contends the trial court abused its discretion when it admitted the videos as animations because they were not fair and accurate representations of the evidence. We disagree.
1. Legal Principles
¶ 44 The division in Cauley held that a computer animation is admissible as demonstrative evidence if the party offering it can (1) authenticate it under CRE 901 ; (2) show that it is relevant under CRE 401 and 402 ; (3) establish that it is a fair and accurate representation of the evidence to which it relates; and (4) demonstrate that its probative value is not substantially outweighed by the danger of unfair prejudice under CRE 403. Cauley, 32 P.3d at 607.
¶ 45 As far as the third factor-fair and accurate depiction-is concerned, an animation must be substantially similar to the event that it depicts to be admissible. See Hinkle, 81 F.3d at 424. "It need not be exact in every detail, but the important elements must be identical or very similar to the scene" as described by the evidence that the proponent of the animation introduces. Clark, 529 S.E.2d at 537. But a court does not have to exclude an animation if it is "inconsistent with testimony or evidence presented by the opposing party" as long as it "fairly and accurately portrays" the proponent's "version of events." Id. So an animation that depicts an automobile collision "must be technically correct on details such as distance, terrain, relative speed, path of travel, and surroundings." Id.
2. Analysis
¶ 46 Defendant asserts that the court should not have admitted the videos because the trooper told the jury that they were "to scale" and that they depicted the "actual scene," even though defendant had disputed certain facts depicted in the animation.
*1035Defendant adds that the videos did not establish how much time would have been necessary for defendant to stop after the collision and that they did not show that defendant had stopped to look around as he had claimed. We generally disagree because we conclude that the prosecution satisfied the four-factor test in Cauley . Turning to defendant's specific contentions, we additionally conclude that, based on the evidence in the record, the videos were admissible because they were substantially similar to the collision that they depicted. See Hinkle, 81 F.3d at 424.
¶ 47 First, the record shows that the videos correctly incorporated details that the trooper had entered into the computer program, such as distances, the surrounding terrain, the relative speeds of the car and the bicycle, and their paths of travel. See Clark, 529 S.E.2d at 537. We conclude that the videos fairly and accurately portrayed the prosecution's version of the collision based on the evidence that the prosecution submitted at trial. See id.
¶ 48 Second, when the trooper testified that the videos were "to scale" and "consistent with the actual scene," he was discussing the interface between Google Earth imagery and the measurements of the actual scene that he had entered into the computer. According to his testimony, the videos' depiction of the terrain was to scale because the computer program automatically coordinated the terrain with the measurements that he had entered. See Serge, 58 Pa. D. & C.4th at 73 ("[I]f the animation purports to contain exact measurements or to be drawn to scale, the party seeking to utilize it must offer testimony as to how the data was obtained and inputted into the computer.").
¶ 49 The relative positions of the bicycle and the car in the videos were based on the trooper's knowledge of the laws of physics' effect on the physical evidence that he had inspected. The relative speeds of the bicycle and the car were based on the posted speed limit and on the information that the bicyclist had provided. The location of the collision and the trajectories of the bicycle and of the victim were likewise based on the bicyclist's description of the collision, the trooper's calculations, and the physical evidence. (Indeed, the trooper testified about these factors at some length.)
¶ 50 Third, the facts that defendant asserts were in dispute do not bear on the videos' purpose, which was to illustrate the trooper's theory of how the collision occurred. See Robinson v. Mo. Pac. R.R. Co., 16 F.3d 1083, 1087 (10th Cir.1994). Defense counsel adequately explored any discrepancies between the videos and defendant's description of the collision, including what defendant could see at that time and whether defendant had stopped after the collision. See id. at 1088 ; Tollardo, 77 P.3d at 1028 ; State v. Geske, 339 Wis.2d 170, 810 N.W.2d 226, 235 (Ct.App.2012). We conclude that these discrepancies were not so significant that the trial court should have excluded the videos. See Clark, 529 S.E.2d at 537.
¶ 51 Fourth, any prejudice that these discrepancies may have caused did not substantially outweigh the videos' probative value. See CRE 403 ; Hinkle, 81 F.3d at 425. To illustrate this point, we note that the jury asked questions during the trooper's testimony that made clear that it understood that the videos were not infallible. For example, the jury asked whether the computer program was "capable of factoring in weather patterns." The trooper replied that the program could not incorporate clouds that the bicyclist said had obscured the sun when it was low on the horizon. And the jury asked if defendant could have looked up and seen the bicyclist immediately after the collision. The trooper responded that it was possible because "the program obviously doesn't completely emulate the peripheral vision of the human eye."
¶ 52 We therefore conclude that the trial court did not abuse its discretion when it admitted the videos into evidence.
III. Restitution
¶ 53 Defendant contends that the trial court abused its discretion when it ordered defendant to pay restitution. We disagree.
A. Standard of Review and Legal Principles
¶ 54 We review a trial court's restitution order for an abuse of discretion.
*1036People v. Martinez, 2015 COA 37, ¶ 29, --- P.3d ----. A court abuses its discretion in ordering restitution if it misinterprets or misapplies the law. People v. Montanez, 2012 COA 101, ¶ 8, 300 P.3d 940.
¶ 55 We liberally construe the restitution statute to accomplish the legislative goal of making victims whole for harms that they have suffered as a result of the defendant's crime. People v. Rivera, 250 P.3d 1272, 1274 (Colo.App.2010). As is pertinent to this case, the definition of a "victim" who may receive restitution includes "[a]ny person who has suffered losses because of a contractual relationship with" the person against whom the offense was committed. § 18-1.3-602(4)(a)(III), C.R.S.2015. This includes an insurer. Id.
¶ 56 The prosecution must establish the amount of restitution by a preponderance of the evidence. Martinez, ¶ 30.
B. Analysis
1. Pain and Suffering
¶ 57 Defendant contends that the trial court ordered him to pay restitution to the bicyclist's insurer for payments that it had made to her to compensate for her pain and suffering. He points to section 18-1.3-602(3)(a), which states that " '[r]estitution' does not include damages for physical or mental pain and suffering." But our review of the record does not show that the trial court ordered defendant to pay restitution to the insurer for the bicyclist's pain and suffering.
¶ 58 The prosecution's restitution motion originally asked for $100,000, or all the money that the bicyclist's insurer had paid her. This amount included payments to compensate the bicyclist for her pain and suffering.
¶ 59 But the court ordered defendant to pay the insurer $37,717.28, which only included the bicyclist's lost wages, the replacement cost of her bicycle and some equipment that was damaged by the collision, and her medical expenses. And the record, such as the testimony of the insurer's subrogation adjuster, makes clear that the lower figure did not include reimbursement for pain and suffering. We therefore conclude that the trial court did not misinterpret or misapply the restitution statute when it entered the restitution order, which leads us next to conclude that the court did not abuse its discretion.
2. The Evidence
¶ 60 Defendant also contends (1) the prosecution did not offer sufficient proof of the amount of restitution; and (2) the court improperly denied him an opportunity to present evidence on his own behalf. We disagree.
¶ 61 First, the record indicates that the prosecution introduced exhibits that supported its restitution request. For example, the subrogation adjustor testified that there was an exhibit 2, which was the insurer's "payout summary of the different transactions." He also referred to an exhibit 1, which was the documentation of the bicyclist's medical bills, her losses, and associated documentation.
¶ 62 But our careful examination of the record has not been able to find exhibits 1 or 2, and neither defendant nor the prosecution has directed us in their briefs to where they may be in the record.
¶ 63 As the appellant, it was defendant's responsibility to include these exhibits in the record. C.A.R. 10(b). We therefore presume that these missing exhibits supported the trial court's restitution order. See People v. Duran, 2015 COA 141, ¶ 12, --- P.3d ---- (stating that facts not appearing in the record cannot be reviewed, and omitted portions are presumed to support the judgment).
¶ 64 Second, the court gave defendant sufficient opportunity to contest the prosecution's restitution request. He filed a motion opposing the request, and he objected to the award on the record. He cross-examined the prosecution's witnesses.
¶ 65 And, although defendant had a right to contest the amount of restitution that the prosecution had requested, the trial court was not required to conduct a "mini-trial" on the issue of restitution. People v. Johnson, 780 P.2d 504, 507 (Colo.1989). So we conclude that the trial court's decision to deny defendant's request to call a witness was not an abuse of discretion, especially because we *1037have presumed above that the insurer's exhibits supported the order.
¶ 66 The judgment and restitution order are affirmed.
JUDGE FURMAN and JUDGE LICHTENSTEIN concur.